FieldKeplerianOrbit.java

  1. /* Copyright 2002-2024 CS GROUP
  2.  * Licensed to CS GROUP (CS) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * CS licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *   http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.orekit.orbits;


  20. import java.lang.reflect.Array;

  22. import org.hipparchus.CalculusFieldElement;
  23. import org.hipparchus.Field;
  24. import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative1;
  25. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  26. import org.hipparchus.util.FastMath;
  27. import org.hipparchus.util.FieldSinCos;
  28. import org.hipparchus.util.MathArrays;
  29. import org.orekit.errors.OrekitException;
  30. import org.orekit.errors.OrekitIllegalArgumentException;
  31. import org.orekit.errors.OrekitInternalError;
  32. import org.orekit.errors.OrekitMessages;
  33. import org.orekit.frames.Frame;
  34. import org.orekit.time.FieldAbsoluteDate;
  35. import org.orekit.utils.FieldPVCoordinates;
  36. import org.orekit.utils.TimeStampedFieldPVCoordinates;


  39. /**
  40.  * This class handles traditional Keplerian orbital parameters.

  42.  * <p>
  43.  * The parameters used internally are the classical Keplerian elements:
  44.  *   <pre>
  45.  *     a
  46.  *     e
  47.  *     i
  48.  *     ω
  49.  *     Ω
  50.  *     v
  51.  *   </pre>
  52.  * where ω stands for the Perigee Argument, Ω stands for the
  53.  * Right Ascension of the Ascending Node and v stands for the true anomaly.
  54.  * <p>
  55.  * This class supports hyperbolic orbits, using the convention that semi major
  56.  * axis is negative for such orbits (and of course eccentricity is greater than 1).
  57.  * </p>
  58.  * <p>
  59.  * When orbit is either equatorial or circular, some Keplerian elements
  60.  * (more precisely ω and Ω) become ambiguous so this class should not
  61.  * be used for such orbits. For this reason, {@link EquinoctialOrbit equinoctial
  62.  * orbits} is the recommended way to represent orbits.
  63.  * </p>

  65.  * <p>
  66.  * The instance <code>KeplerianOrbit</code> is guaranteed to be immutable.
  67.  * </p>
  68.  * @see     Orbit
  69.  * @see    CircularOrbit
  70.  * @see    CartesianOrbit
  71.  * @see    EquinoctialOrbit
  72.  * @author Luc Maisonobe
  73.  * @author Guylaine Prat
  74.  * @author Fabien Maussion
  75.  * @author V&eacute;ronique Pommier-Maurussane
  76.  * @author Andrea Antolino
  77.  * @since 9.0
  78.  * @param <T> type of the field elements
  79.  */
  80. public class FieldKeplerianOrbit<T extends CalculusFieldElement<T>> extends FieldOrbit<T>
  81.         implements PositionAngleBased {

  83.     /** Name of the eccentricity parameter. */
  84.     private static final String ECCENTRICITY = "eccentricity";

  86.     /** Semi-major axis (m). */
  87.     private final T a;

  89.     /** Eccentricity. */
  90.     private final T e;

  92.     /** Inclination (rad). */
  93.     private final T i;

  95.     /** Perigee Argument (rad). */
  96.     private final T pa;

  98.     /** Right Ascension of Ascending Node (rad). */
  99.     private final T raan;

  101.     /** Cached anomaly (rad). */
  102.     private final T cachedAnomaly;

  104.     /** Semi-major axis derivative (m/s). */
  105.     private final T aDot;

  107.     /** Eccentricity derivative. */
  108.     private final T eDot;

  110.     /** Inclination derivative (rad/s). */
  111.     private final T iDot;

  113.     /** Perigee Argument derivative (rad/s). */
  114.     private final T paDot;

  116.     /** Right Ascension of Ascending Node derivative (rad/s). */
  117.     private final T raanDot;

  119.     /** Derivative of cached anomaly (rad/s). */
  120.     private final T cachedAnomalyDot;

  122.     /** Cached type of position angle. */
  123.     private final PositionAngleType cachedPositionAngleType;

  125.     /** Partial Cartesian coordinates (position and velocity are valid, acceleration may be missing). */
  126.     private FieldPVCoordinates<T> partialPV;

  128.     /** PThird Canonical Vector. */
  129.     private final FieldVector3D<T> PLUS_K;

  131.     /** Creates a new instance.
  132.      * @param a  semi-major axis (m), negative for hyperbolic orbits
  133.      * @param e eccentricity (positive or equal to 0)
  134.      * @param i inclination (rad)
  135.      * @param pa perigee argument (ω, rad)
  136.      * @param raan right ascension of ascending node (Ω, rad)
  137.      * @param anomaly mean, eccentric or true anomaly (rad)
  138.      * @param type type of anomaly
  139.      * @param cachedPositionAngleType type of cached anomaly
  140.      * @param frame the frame in which the parameters are defined
  141.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  142.      * @param date date of the orbital parameters
  143.      * @param mu central attraction coefficient (m³/s²)
  144.      * @exception IllegalArgumentException if frame is not a {@link
  145.      * Frame#isPseudoInertial pseudo-inertial frame} or a and e don't match for hyperbolic orbits,
  146.      * or v is out of range for hyperbolic orbits
  147.      * @since 12.1
  148.      */
  149.     public FieldKeplerianOrbit(final T a, final T e, final T i,
  150.                                final T pa, final T raan,
  151.                                final T anomaly, final PositionAngleType type,
  152.                                final PositionAngleType cachedPositionAngleType,
  153.                                final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
  154.         throws IllegalArgumentException {
  155.         this(a, e, i, pa, raan, anomaly,
  156.              null, null, null, null, null, null,
  157.              type, cachedPositionAngleType, frame, date, mu);
  158.     }

  160.     /** Creates a new instance.
  161.      * @param a  semi-major axis (m), negative for hyperbolic orbits
  162.      * @param e eccentricity (positive or equal to 0)
  163.      * @param i inclination (rad)
  164.      * @param pa perigee argument (ω, rad)
  165.      * @param raan right ascension of ascending node (Ω, rad)
  166.      * @param anomaly mean, eccentric or true anomaly (rad)
  167.      * @param type type of anomaly
  168.      * @param frame the frame in which the parameters are defined
  169.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  170.      * @param date date of the orbital parameters
  171.      * @param mu central attraction coefficient (m³/s²)
  172.      * @exception IllegalArgumentException if frame is not a {@link
  173.      * Frame#isPseudoInertial pseudo-inertial frame} or a and e don't match for hyperbolic orbits,
  174.      * or v is out of range for hyperbolic orbits
  175.      * @since 12.1
  176.      */
  177.     public FieldKeplerianOrbit(final T a, final T e, final T i,
  178.                                final T pa, final T raan,
  179.                                final T anomaly, final PositionAngleType type,
  180.                                final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
  181.             throws IllegalArgumentException {
  182.         this(a, e, i, pa, raan, anomaly, type, type, frame, date, mu);
  183.     }

  185.     /** Creates a new instance.
  186.      * @param a  semi-major axis (m), negative for hyperbolic orbits
  187.      * @param e eccentricity (positive or equal to 0)
  188.      * @param i inclination (rad)
  189.      * @param pa perigee argument (ω, rad)
  190.      * @param raan right ascension of ascending node (Ω, rad)
  191.      * @param anomaly mean, eccentric or true anomaly (rad)
  192.      * @param aDot  semi-major axis derivative, null if unknown (m/s)
  193.      * @param eDot eccentricity derivative, null if unknown
  194.      * @param iDot inclination derivative, null if unknown (rad/s)
  195.      * @param paDot perigee argument derivative, null if unknown (rad/s)
  196.      * @param raanDot right ascension of ascending node derivative, null if unknown (rad/s)
  197.      * @param anomalyDot mean, eccentric or true anomaly derivative, null if unknown (rad/s)
  198.      * @param type type of anomaly
  199.      * @param cachedPositionAngleType type of cached anomaly
  200.      * @param frame the frame in which the parameters are defined
  201.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  202.      * @param date date of the orbital parameters
  203.      * @param mu central attraction coefficient (m³/s²)
  204.      * @exception IllegalArgumentException if frame is not a {@link
  205.      * Frame#isPseudoInertial pseudo-inertial frame} or a and e don't match for hyperbolic orbits,
  206.      * or v is out of range for hyperbolic orbits
  207.      * @since 12.1
  208.      */
  209.     public FieldKeplerianOrbit(final T a, final T e, final T i,
  210.                                final T pa, final T raan, final T anomaly,
  211.                                final T aDot, final T eDot, final T iDot,
  212.                                final T paDot, final T raanDot, final T anomalyDot,
  213.                                final PositionAngleType type, final PositionAngleType cachedPositionAngleType,
  214.                                final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
  215.         throws IllegalArgumentException {
  216.         super(frame, date, mu);
  217.         this.cachedPositionAngleType = cachedPositionAngleType;

  219.         if (a.multiply(e.negate().add(1)).getReal() < 0) {
  220.             throw new OrekitIllegalArgumentException(OrekitMessages.ORBIT_A_E_MISMATCH_WITH_CONIC_TYPE, a.getReal(), e.getReal());
  221.         }

  223.         // Checking eccentricity range
  224.         checkParameterRangeInclusive(ECCENTRICITY, e.getReal(), 0.0, Double.POSITIVE_INFINITY);

  226.         this.a       =    a;
  227.         this.aDot    =    aDot;
  228.         this.e       =    e;
  229.         this.eDot    =    eDot;
  230.         this.i       =    i;
  231.         this.iDot    =    iDot;
  232.         this.pa      =    pa;
  233.         this.paDot   =    paDot;
  234.         this.raan    =    raan;
  235.         this.raanDot =    raanDot;

  237.         this.PLUS_K = FieldVector3D.getPlusK(a.getField());  // third canonical vector

  239.         if (hasDerivatives()) {
  240.             final FieldUnivariateDerivative1<T> cachedAnomalyUD = initializeCachedAnomaly(anomaly, anomalyDot, type);
  241.             this.cachedAnomaly = cachedAnomalyUD.getValue();
  242.             this.cachedAnomalyDot = cachedAnomalyUD.getFirstDerivative();
  243.         } else {
  244.             this.cachedAnomaly = initializeCachedAnomaly(anomaly, type);
  245.             this.cachedAnomalyDot = null;
  246.         }

  248.         // check true anomaly range
  249.         if (!isElliptical()) {
  250.             final T trueAnomaly = getTrueAnomaly();
  251.             if (e.multiply(trueAnomaly.cos()).add(1).getReal() <= 0) {
  252.                 final double vMax = e.reciprocal().negate().acos().getReal();
  253.                 throw new OrekitIllegalArgumentException(OrekitMessages.ORBIT_ANOMALY_OUT_OF_HYPERBOLIC_RANGE,
  254.                         trueAnomaly.getReal(), e.getReal(), -vMax, vMax);
  255.             }
  256.         }

  258.         this.partialPV = null;

  260.     }

  262.     /** Creates a new instance.
  263.      * @param a  semi-major axis (m), negative for hyperbolic orbits
  264.      * @param e eccentricity (positive or equal to 0)
  265.      * @param i inclination (rad)
  266.      * @param pa perigee argument (ω, rad)
  267.      * @param raan right ascension of ascending node (Ω, rad)
  268.      * @param anomaly mean, eccentric or true anomaly (rad)
  269.      * @param aDot  semi-major axis derivative, null if unknown (m/s)
  270.      * @param eDot eccentricity derivative, null if unknown
  271.      * @param iDot inclination derivative, null if unknown (rad/s)
  272.      * @param paDot perigee argument derivative, null if unknown (rad/s)
  273.      * @param raanDot right ascension of ascending node derivative, null if unknown (rad/s)
  274.      * @param anomalyDot mean, eccentric or true anomaly derivative, null if unknown (rad/s)
  275.      * @param type type of anomaly
  276.      * @param frame the frame in which the parameters are defined
  277.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  278.      * @param date date of the orbital parameters
  279.      * @param mu central attraction coefficient (m³/s²)
  280.      * @exception IllegalArgumentException if frame is not a {@link
  281.      * Frame#isPseudoInertial pseudo-inertial frame} or a and e don't match for hyperbolic orbits,
  282.      * or v is out of range for hyperbolic orbits
  283.      */
  284.     public FieldKeplerianOrbit(final T a, final T e, final T i,
  285.                                final T pa, final T raan, final T anomaly,
  286.                                final T aDot, final T eDot, final T iDot,
  287.                                final T paDot, final T raanDot, final T anomalyDot,
  288.                                final PositionAngleType type,
  289.                                final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
  290.             throws IllegalArgumentException {
  291.         this(a, e, i, pa, raan, anomaly, aDot, eDot, iDot, paDot, raanDot, anomalyDot,
  292.                 type, type, frame, date, mu);
  293.     }

  295.     /** Constructor from Cartesian parameters.
  296.      *
  297.      * <p> The acceleration provided in {@code FieldPVCoordinates} is accessible using
  298.      * {@link #getPVCoordinates()} and {@link #getPVCoordinates(Frame)}. All other methods
  299.      * use {@code mu} and the position to compute the acceleration, including
  300.      * {@link #shiftedBy(CalculusFieldElement)} and {@link #getPVCoordinates(FieldAbsoluteDate, Frame)}.
  301.      *
  302.      * @param pvCoordinates the PVCoordinates of the satellite
  303.      * @param frame the frame in which are defined the {@link FieldPVCoordinates}
  304.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  305.      * @param mu central attraction coefficient (m³/s²)
  306.      * @exception IllegalArgumentException if frame is not a {@link
  307.      * Frame#isPseudoInertial pseudo-inertial frame}
  308.      */
  309.     public FieldKeplerianOrbit(final TimeStampedFieldPVCoordinates<T> pvCoordinates,
  310.                                final Frame frame, final T mu)
  311.         throws IllegalArgumentException {
  312.         this(pvCoordinates, frame, mu, hasNonKeplerianAcceleration(pvCoordinates, mu));
  313.     }

  315.     /** Constructor from Cartesian parameters.
  316.      *
  317.      * <p> The acceleration provided in {@code FieldPVCoordinates} is accessible using
  318.      * {@link #getPVCoordinates()} and {@link #getPVCoordinates(Frame)}. All other methods
  319.      * use {@code mu} and the position to compute the acceleration, including
  320.      * {@link #shiftedBy(CalculusFieldElement)} and {@link #getPVCoordinates(FieldAbsoluteDate, Frame)}.
  321.      *
  322.      * @param pvCoordinates the PVCoordinates of the satellite
  323.      * @param frame the frame in which are defined the {@link FieldPVCoordinates}
  324.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  325.      * @param mu central attraction coefficient (m³/s²)
  326.      * @param reliableAcceleration if true, the acceleration is considered to be reliable
  327.      * @exception IllegalArgumentException if frame is not a {@link
  328.      * Frame#isPseudoInertial pseudo-inertial frame}
  329.      */
  330.     private FieldKeplerianOrbit(final TimeStampedFieldPVCoordinates<T> pvCoordinates,
  331.                                 final Frame frame, final T mu,
  332.                                 final boolean reliableAcceleration)
  333.         throws IllegalArgumentException {

  335.         super(pvCoordinates, frame, mu);

  337.         // third canonical vector
  338.         this.PLUS_K = FieldVector3D.getPlusK(getOne().getField());

  340.         // compute inclination
  341.         final FieldVector3D<T> momentum = pvCoordinates.getMomentum();
  342.         final T m2 = momentum.getNormSq();

  344.         i = FieldVector3D.angle(momentum, PLUS_K);
  345.         // compute right ascension of ascending node
  346.         raan = FieldVector3D.crossProduct(PLUS_K, momentum).getAlpha();
  347.         // preliminary computations for parameters depending on orbit shape (elliptic or hyperbolic)
  348.         final FieldVector3D<T> pvP     = pvCoordinates.getPosition();
  349.         final FieldVector3D<T> pvV     = pvCoordinates.getVelocity();
  350.         final FieldVector3D<T> pvA     = pvCoordinates.getAcceleration();

  352.         final T   r2      = pvP.getNormSq();
  353.         final T   r       = r2.sqrt();
  354.         final T   V2      = pvV.getNormSq();
  355.         final T   rV2OnMu = r.multiply(V2).divide(mu);

  357.         // compute semi-major axis (will be negative for hyperbolic orbits)
  358.         a = r.divide(rV2OnMu.negate().add(2.0));
  359.         final T muA = a.multiply(mu);

  361.         // compute true anomaly
  362.         if (isElliptical()) {
  363.             // elliptic or circular orbit
  364.             final T eSE = FieldVector3D.dotProduct(pvP, pvV).divide(muA.sqrt());
  365.             final T eCE = rV2OnMu.subtract(1);
  366.             e = (eSE.multiply(eSE).add(eCE.multiply(eCE))).sqrt();
  367.             this.cachedPositionAngleType = PositionAngleType.ECCENTRIC;
  368.             cachedAnomaly = eSE.atan2(eCE);
  369.         } else {
  370.             // hyperbolic orbit
  371.             final T eSH = FieldVector3D.dotProduct(pvP, pvV).divide(muA.negate().sqrt());
  372.             final T eCH = rV2OnMu.subtract(1);
  373.             e = (m2.negate().divide(muA).add(1)).sqrt();
  374.             this.cachedPositionAngleType = PositionAngleType.TRUE;
  375.             cachedAnomaly = FieldKeplerianAnomalyUtility.hyperbolicEccentricToTrue(e, (eCH.add(eSH)).divide(eCH.subtract(eSH)).log().divide(2));
  376.         }

  378.         // Checking eccentricity range
  379.         checkParameterRangeInclusive(ECCENTRICITY, e.getReal(), 0.0, Double.POSITIVE_INFINITY);

  381.         // compute perigee argument
  382.         final FieldVector3D<T> node = new FieldVector3D<>(raan, getZero());
  383.         final T px = FieldVector3D.dotProduct(pvP, node);
  384.         final T py = FieldVector3D.dotProduct(pvP, FieldVector3D.crossProduct(momentum, node)).divide(m2.sqrt());
  385.         pa = py.atan2(px).subtract(getTrueAnomaly());

  387.         partialPV = pvCoordinates;

  389.         if (reliableAcceleration) {
  390.             // we have a relevant acceleration, we can compute derivatives

  392.             final T[][] jacobian = MathArrays.buildArray(a.getField(), 6, 6);
  393.             getJacobianWrtCartesian(PositionAngleType.MEAN, jacobian);

  395.             final FieldVector3D<T> keplerianAcceleration    = new FieldVector3D<>(r.multiply(r2).reciprocal().multiply(mu.negate()), pvP);
  396.             final FieldVector3D<T> nonKeplerianAcceleration = pvA.subtract(keplerianAcceleration);
  397.             final T   aX                       = nonKeplerianAcceleration.getX();
  398.             final T   aY                       = nonKeplerianAcceleration.getY();
  399.             final T   aZ                       = nonKeplerianAcceleration.getZ();
  400.             aDot    = jacobian[0][3].multiply(aX).add(jacobian[0][4].multiply(aY)).add(jacobian[0][5].multiply(aZ));
  401.             eDot    = jacobian[1][3].multiply(aX).add(jacobian[1][4].multiply(aY)).add(jacobian[1][5].multiply(aZ));
  402.             iDot    = jacobian[2][3].multiply(aX).add(jacobian[2][4].multiply(aY)).add(jacobian[2][5].multiply(aZ));
  403.             paDot   = jacobian[3][3].multiply(aX).add(jacobian[3][4].multiply(aY)).add(jacobian[3][5].multiply(aZ));
  404.             raanDot = jacobian[4][3].multiply(aX).add(jacobian[4][4].multiply(aY)).add(jacobian[4][5].multiply(aZ));

  406.             // in order to compute true anomaly derivative, we must compute
  407.             // mean anomaly derivative including Keplerian motion and convert to true anomaly
  408.             final T MDot = getKeplerianMeanMotion().
  409.                            add(jacobian[5][3].multiply(aX)).add(jacobian[5][4].multiply(aY)).add(jacobian[5][5].multiply(aZ));
  410.             final FieldUnivariateDerivative1<T> eUD = new FieldUnivariateDerivative1<>(e, eDot);
  411.             final FieldUnivariateDerivative1<T> MUD = new FieldUnivariateDerivative1<>(getMeanAnomaly(), MDot);
  412.             if (cachedPositionAngleType == PositionAngleType.ECCENTRIC) {
  413.                 final FieldUnivariateDerivative1<T> EUD = (a.getReal() < 0) ?
  414.                          FieldKeplerianAnomalyUtility.hyperbolicMeanToEccentric(eUD, MUD) :
  415.                          FieldKeplerianAnomalyUtility.ellipticMeanToEccentric(eUD, MUD);
  416.                 cachedAnomalyDot = EUD.getFirstDerivative();
  417.             } else { // TRUE
  418.                 final FieldUnivariateDerivative1<T> vUD = (a.getReal() < 0) ?
  419.                          FieldKeplerianAnomalyUtility.hyperbolicMeanToTrue(eUD, MUD) :
  420.                          FieldKeplerianAnomalyUtility.ellipticMeanToTrue(eUD, MUD);
  421.                 cachedAnomalyDot = vUD.getFirstDerivative();
  422.             }

  424.         } else {
  425.             // acceleration is either almost zero or NaN,
  426.             // we assume acceleration was not known
  427.             // we don't set up derivatives
  428.             aDot    = null;
  429.             eDot    = null;
  430.             iDot    = null;
  431.             paDot   = null;
  432.             raanDot = null;
  433.             cachedAnomalyDot    = null;
  434.         }

  436.     }

  438.     /** Constructor from Cartesian parameters.
  439.      *
  440.      * <p> The acceleration provided in {@code FieldPVCoordinates} is accessible using
  441.      * {@link #getPVCoordinates()} and {@link #getPVCoordinates(Frame)}. All other methods
  442.      * use {@code mu} and the position to compute the acceleration, including
  443.      * {@link #shiftedBy(CalculusFieldElement)} and {@link #getPVCoordinates(FieldAbsoluteDate, Frame)}.
  444.      *
  445.      * @param FieldPVCoordinates the PVCoordinates of the satellite
  446.      * @param frame the frame in which are defined the {@link FieldPVCoordinates}
  447.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  448.      * @param date date of the orbital parameters
  449.      * @param mu central attraction coefficient (m³/s²)
  450.      * @exception IllegalArgumentException if frame is not a {@link
  451.      * Frame#isPseudoInertial pseudo-inertial frame}
  452.      */
  453.     public FieldKeplerianOrbit(final FieldPVCoordinates<T> FieldPVCoordinates,
  454.                                final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
  455.         throws IllegalArgumentException {
  456.         this(new TimeStampedFieldPVCoordinates<>(date, FieldPVCoordinates), frame, mu);
  457.     }

  459.     /** Constructor from any kind of orbital parameters.
  460.      * @param op orbital parameters to copy
  461.      */
  462.     public FieldKeplerianOrbit(final FieldOrbit<T> op) {
  463.         this(op.getPVCoordinates(), op.getFrame(), op.getMu(), op.hasDerivatives());
  464.     }

  466.     /** Constructor from Field and KeplerianOrbit.
  467.      * <p>Build a FieldKeplerianOrbit from non-Field KeplerianOrbit.</p>
  468.      * @param field CalculusField to base object on
  469.      * @param op non-field orbit with only "constant" terms
  470.      * @since 12.0
  471.      */
  472.     public FieldKeplerianOrbit(final Field<T> field, final KeplerianOrbit op) {
  473.         this(field.getZero().newInstance(op.getA()), field.getZero().newInstance(op.getE()), field.getZero().newInstance(op.getI()),
  474.                 field.getZero().newInstance(op.getPerigeeArgument()), field.getZero().newInstance(op.getRightAscensionOfAscendingNode()),
  475.                 field.getZero().newInstance(op.getAnomaly(op.getCachedPositionAngleType())),
  476.                 (op.hasDerivatives()) ? field.getZero().newInstance(op.getADot()) : null,
  477.                 (op.hasDerivatives()) ? field.getZero().newInstance(op.getEDot()) : null,
  478.                 (op.hasDerivatives()) ? field.getZero().newInstance(op.getIDot()) : null,
  479.                 (op.hasDerivatives()) ? field.getZero().newInstance(op.getPerigeeArgumentDot()) : null,
  480.                 (op.hasDerivatives()) ? field.getZero().newInstance(op.getRightAscensionOfAscendingNodeDot()) : null,
  481.                 (op.hasDerivatives()) ? field.getZero().newInstance(op.getAnomalyDot(op.getCachedPositionAngleType())) : null,
  482.                 op.getCachedPositionAngleType(), op.getFrame(),
  483.                 new FieldAbsoluteDate<>(field, op.getDate()), field.getZero().newInstance(op.getMu()));
  484.     }

  486.     /** Constructor from Field and Orbit.
  487.      * <p>Build a FieldKeplerianOrbit from any non-Field Orbit.</p>
  488.      * @param field CalculusField to base object on
  489.      * @param op non-field orbit with only "constant" terms
  490.      * @since 12.0
  491.      */
  492.     public FieldKeplerianOrbit(final Field<T> field, final Orbit op) {
  493.         this(field, (KeplerianOrbit) OrbitType.KEPLERIAN.convertType(op));
  494.     }

  496.     /** {@inheritDoc} */
  497.     @Override
  498.     public OrbitType getType() {
  499.         return OrbitType.KEPLERIAN;
  500.     }

  502.     /** {@inheritDoc} */
  503.     @Override
  504.     public T getA() {
  505.         return a;
  506.     }

  508.     /** {@inheritDoc} */
  509.     @Override
  510.     public T getADot() {
  511.         return aDot;
  512.     }

  514.     /** {@inheritDoc} */
  515.     @Override
  516.     public T getE() {
  517.         return e;
  518.     }

  520.     /** {@inheritDoc} */
  521.     @Override
  522.     public T getEDot() {
  523.         return eDot;
  524.     }

  526.     /** {@inheritDoc} */
  527.     @Override
  528.     public T getI() {
  529.         return i;
  530.     }

  532.     /** {@inheritDoc} */
  533.     @Override
  534.     public T getIDot() {
  535.         return iDot;
  536.     }

  538.     /** Get the perigee argument.
  539.      * @return perigee argument (rad)
  540.      */
  541.     public T getPerigeeArgument() {
  542.         return pa;
  543.     }

  545.     /** Get the perigee argument derivative.
  546.      * <p>
  547.      * If the orbit was created without derivatives, the value returned is null.
  548.      * </p>
  549.      * @return perigee argument derivative (rad/s)
  550.      */
  551.     public T getPerigeeArgumentDot() {
  552.         return paDot;
  553.     }

  555.     /** Get the right ascension of the ascending node.
  556.      * @return right ascension of the ascending node (rad)
  557.      */
  558.     public T getRightAscensionOfAscendingNode() {
  559.         return raan;
  560.     }

  562.     /** Get the right ascension of the ascending node derivative.
  563.      * <p>
  564.      * If the orbit was created without derivatives, the value returned is null.
  565.      * </p>
  566.      * @return right ascension of the ascending node derivative (rad/s)
  567.      */
  568.     public T getRightAscensionOfAscendingNodeDot() {
  569.         return raanDot;
  570.     }

  572.     /** Get the true anomaly.
  573.      * @return true anomaly (rad)
  574.      */
  575.     public T getTrueAnomaly() {
  576.         switch (cachedPositionAngleType) {
  577.             case MEAN: return (a.getReal() < 0) ? FieldKeplerianAnomalyUtility.hyperbolicMeanToTrue(e, cachedAnomaly) :
  578.                     FieldKeplerianAnomalyUtility.ellipticMeanToTrue(e, cachedAnomaly);

  580.             case TRUE: return cachedAnomaly;

  582.             case ECCENTRIC: return (a.getReal() < 0) ? FieldKeplerianAnomalyUtility.hyperbolicEccentricToTrue(e, cachedAnomaly) :
  583.                     FieldKeplerianAnomalyUtility.ellipticEccentricToTrue(e, cachedAnomaly);

  585.             default: throw new OrekitInternalError(null);
  586.         }
  587.     }

  589.     /** Get the true anomaly derivative.
  590.      * <p>
  591.      * If the orbit was created without derivatives, the value returned is null.
  592.      * </p>
  593.      * @return true anomaly derivative (rad/s)
  594.      */
  595.     public T getTrueAnomalyDot() {
  596.         if (hasDerivatives()) {
  597.             switch (cachedPositionAngleType) {
  598.                 case MEAN:
  599.                     final FieldUnivariateDerivative1<T> eUD = new FieldUnivariateDerivative1<>(e, eDot);
  600.                     final FieldUnivariateDerivative1<T> MUD = new FieldUnivariateDerivative1<>(cachedAnomaly, cachedAnomalyDot);
  601.                     final FieldUnivariateDerivative1<T> vUD = (a.getReal() < 0) ?
  602.                              FieldKeplerianAnomalyUtility.hyperbolicMeanToTrue(eUD, MUD) :
  603.                              FieldKeplerianAnomalyUtility.ellipticMeanToTrue(eUD, MUD);
  604.                     return vUD.getFirstDerivative();

  606.                 case TRUE:
  607.                     return cachedAnomalyDot;

  609.                 case ECCENTRIC:
  610.                     final FieldUnivariateDerivative1<T> eUD2 = new FieldUnivariateDerivative1<>(e, eDot);
  611.                     final FieldUnivariateDerivative1<T> EUD = new FieldUnivariateDerivative1<>(cachedAnomaly, cachedAnomalyDot);
  612.                     final FieldUnivariateDerivative1<T> vUD2 = (a.getReal() < 0) ?
  613.                              FieldKeplerianAnomalyUtility.hyperbolicEccentricToTrue(eUD2, EUD) :
  614.                              FieldKeplerianAnomalyUtility.ellipticEccentricToTrue(eUD2, EUD);
  615.                     return vUD2.getFirstDerivative();

  617.                 default:
  618.                     throw new OrekitInternalError(null);
  619.             }
  620.         } else {
  621.             return null;
  622.         }
  623.     }

  625.     /** Get the eccentric anomaly.
  626.      * @return eccentric anomaly (rad)
  627.      */
  628.     public T getEccentricAnomaly() {
  629.         switch (cachedPositionAngleType) {
  630.             case MEAN:
  631.                 return (a.getReal() < 0) ? FieldKeplerianAnomalyUtility.hyperbolicMeanToEccentric(e, cachedAnomaly) :
  632.                     FieldKeplerianAnomalyUtility.ellipticMeanToEccentric(e, cachedAnomaly);

  634.             case ECCENTRIC:
  635.                 return cachedAnomaly;

  637.             case TRUE:
  638.                 return (a.getReal() < 0) ? FieldKeplerianAnomalyUtility.hyperbolicTrueToEccentric(e, cachedAnomaly) :
  639.                     FieldKeplerianAnomalyUtility.ellipticTrueToEccentric(e, cachedAnomaly);

  641.             default:
  642.                 throw new OrekitInternalError(null);
  643.         }
  644.     }

  646.     /** Get the eccentric anomaly derivative.
  647.      * <p>
  648.      * If the orbit was created without derivatives, the value returned is null.
  649.      * </p>
  650.      * @return eccentric anomaly derivative (rad/s)
  651.      */
  652.     public T getEccentricAnomalyDot() {
  653.         if (hasDerivatives()) {
  654.             switch (cachedPositionAngleType) {
  655.                 case ECCENTRIC:
  656.                     return cachedAnomalyDot;

  658.                 case TRUE:
  659.                     final FieldUnivariateDerivative1<T> eUD = new FieldUnivariateDerivative1<>(e, eDot);
  660.                     final FieldUnivariateDerivative1<T> vUD = new FieldUnivariateDerivative1<>(cachedAnomaly, cachedAnomalyDot);
  661.                     final FieldUnivariateDerivative1<T> EUD = (a.getReal() < 0) ?
  662.                              FieldKeplerianAnomalyUtility.hyperbolicTrueToEccentric(eUD, vUD) :
  663.                              FieldKeplerianAnomalyUtility.ellipticTrueToEccentric(eUD, vUD);
  664.                     return EUD.getFirstDerivative();

  666.                 case MEAN:
  667.                     final FieldUnivariateDerivative1<T> eUD2 = new FieldUnivariateDerivative1<>(e, eDot);
  668.                     final FieldUnivariateDerivative1<T> MUD = new FieldUnivariateDerivative1<>(cachedAnomaly, cachedAnomalyDot);
  669.                     final FieldUnivariateDerivative1<T> EUD2 = (a.getReal() < 0) ?
  670.                              FieldKeplerianAnomalyUtility.hyperbolicMeanToEccentric(eUD2, MUD) :
  671.                              FieldKeplerianAnomalyUtility.ellipticMeanToEccentric(eUD2, MUD);
  672.                     return EUD2.getFirstDerivative();

  674.                 default:
  675.                     throw new OrekitInternalError(null);
  676.             }
  677.         } else {
  678.             return null;
  679.         }
  680.     }

  682.     /** Get the mean anomaly.
  683.      * @return mean anomaly (rad)
  684.      */
  685.     public T getMeanAnomaly() {
  686.         switch (cachedPositionAngleType) {
  687.             case ECCENTRIC: return (a.getReal() < 0) ? FieldKeplerianAnomalyUtility.hyperbolicEccentricToMean(e, cachedAnomaly) :
  688.                     FieldKeplerianAnomalyUtility.ellipticEccentricToMean(e, cachedAnomaly);

  690.             case MEAN: return cachedAnomaly;

  692.             case TRUE: return (a.getReal() < 0) ? FieldKeplerianAnomalyUtility.hyperbolicTrueToMean(e, cachedAnomaly) :
  693.                     FieldKeplerianAnomalyUtility.ellipticTrueToMean(e, cachedAnomaly);

  695.             default: throw new OrekitInternalError(null);
  696.         }
  697.     }

  699.     /** Get the mean anomaly derivative.
  700.      * <p>
  701.      * If the orbit was created without derivatives, the value returned is null.
  702.      * </p>
  703.      * @return mean anomaly derivative (rad/s)
  704.      */
  705.     public T getMeanAnomalyDot() {
  706.         if (hasDerivatives()) {
  707.             switch (cachedPositionAngleType) {
  708.                 case MEAN:
  709.                     return cachedAnomalyDot;

  711.                 case ECCENTRIC:
  712.                     final FieldUnivariateDerivative1<T> eUD = new FieldUnivariateDerivative1<>(e, eDot);
  713.                     final FieldUnivariateDerivative1<T> EUD = new FieldUnivariateDerivative1<>(cachedAnomaly, cachedAnomalyDot);
  714.                     final FieldUnivariateDerivative1<T> MUD = (a.getReal() < 0) ?
  715.                              FieldKeplerianAnomalyUtility.hyperbolicEccentricToMean(eUD, EUD) :
  716.                              FieldKeplerianAnomalyUtility.ellipticEccentricToMean(eUD, EUD);
  717.                     return MUD.getFirstDerivative();

  719.                 case TRUE:
  720.                     final FieldUnivariateDerivative1<T> eUD2 = new FieldUnivariateDerivative1<>(e, eDot);
  721.                     final FieldUnivariateDerivative1<T> vUD = new FieldUnivariateDerivative1<>(cachedAnomaly, cachedAnomalyDot);
  722.                     final FieldUnivariateDerivative1<T> MUD2 = (a.getReal() < 0) ?
  723.                              FieldKeplerianAnomalyUtility.hyperbolicTrueToMean(eUD2, vUD) :
  724.                              FieldKeplerianAnomalyUtility.ellipticTrueToMean(eUD2, vUD);
  725.                     return MUD2.getFirstDerivative();

  727.                 default:
  728.                     throw new OrekitInternalError(null);
  729.             }
  730.         } else {
  731.             return null;
  732.         }
  733.     }

  735.     /** Get the anomaly.
  736.      * @param type type of the angle
  737.      * @return anomaly (rad)
  738.      */
  739.     public T getAnomaly(final PositionAngleType type) {
  740.         return (type == PositionAngleType.MEAN) ? getMeanAnomaly() :
  741.                                               ((type == PositionAngleType.ECCENTRIC) ? getEccentricAnomaly() :
  742.                                                                                    getTrueAnomaly());
  743.     }

  745.     /** Get the anomaly derivative.
  746.      * <p>
  747.      * If the orbit was created without derivatives, the value returned is null.
  748.      * </p>
  749.      * @param type type of the angle
  750.      * @return anomaly derivative (rad/s)
  751.      */
  752.     public T getAnomalyDot(final PositionAngleType type) {
  753.         return (type == PositionAngleType.MEAN) ? getMeanAnomalyDot() :
  754.                                               ((type == PositionAngleType.ECCENTRIC) ? getEccentricAnomalyDot() :
  755.                                                                                    getTrueAnomalyDot());
  756.     }

  758.     /** {@inheritDoc} */
  759.     @Override
  760.     public boolean hasDerivatives() {
  761.         return aDot != null;
  762.     }

  764.     /** {@inheritDoc} */
  765.     @Override
  766.     public T getEquinoctialEx() {
  767.         return e.multiply(pa.add(raan).cos());
  768.     }

  770.     /** {@inheritDoc} */
  771.     @Override
  772.     public T getEquinoctialExDot() {

  774.         if (!hasDerivatives()) {
  775.             return null;
  776.         }

  778.         final FieldUnivariateDerivative1<T> eUD    = new FieldUnivariateDerivative1<>(e,    eDot);
  779.         final FieldUnivariateDerivative1<T> paUD   = new FieldUnivariateDerivative1<>(pa,   paDot);
  780.         final FieldUnivariateDerivative1<T> raanUD = new FieldUnivariateDerivative1<>(raan, raanDot);
  781.         return eUD.multiply(paUD.add(raanUD).cos()).getFirstDerivative();

  783.     }

  785.     /** {@inheritDoc} */
  786.     @Override
  787.     public T getEquinoctialEy() {
  788.         return e.multiply((pa.add(raan)).sin());
  789.     }

  791.     /** {@inheritDoc} */
  792.     @Override
  793.     public T getEquinoctialEyDot() {

  795.         if (!hasDerivatives()) {
  796.             return null;
  797.         }

  799.         final FieldUnivariateDerivative1<T> eUD    = new FieldUnivariateDerivative1<>(e,    eDot);
  800.         final FieldUnivariateDerivative1<T> paUD   = new FieldUnivariateDerivative1<>(pa,   paDot);
  801.         final FieldUnivariateDerivative1<T> raanUD = new FieldUnivariateDerivative1<>(raan, raanDot);
  802.         return eUD.multiply(paUD.add(raanUD).sin()).getFirstDerivative();

  804.     }

  806.     /** {@inheritDoc} */
  807.     @Override
  808.     public T getHx() {
  809.         // Check for equatorial retrograde orbit
  810.         if (FastMath.abs(i.subtract(i.getPi()).getReal()) < 1.0e-10) {
  811.             return getZero().add(Double.NaN);
  812.         }
  813.         return raan.cos().multiply(i.divide(2).tan());
  814.     }

  816.     /** {@inheritDoc} */
  817.     @Override
  818.     public T getHxDot() {

  820.         if (!hasDerivatives()) {
  821.             return null;
  822.         }

  824.         // Check for equatorial retrograde orbit
  825.         if (FastMath.abs(i.subtract(i.getPi()).getReal()) < 1.0e-10) {
  826.             return getZero().add(Double.NaN);
  827.         }

  829.         final FieldUnivariateDerivative1<T> iUD    = new FieldUnivariateDerivative1<>(i,    iDot);
  830.         final FieldUnivariateDerivative1<T> raanUD = new FieldUnivariateDerivative1<>(raan, raanDot);
  831.         return raanUD.cos().multiply(iUD.multiply(0.5).tan()).getFirstDerivative();

  833.     }

  835.     /** {@inheritDoc} */
  836.     @Override
  837.     public T getHy() {
  838.         // Check for equatorial retrograde orbit
  839.         if (FastMath.abs(i.subtract(i.getPi()).getReal()) < 1.0e-10) {
  840.             return getZero().add(Double.NaN);
  841.         }
  842.         return raan.sin().multiply(i.divide(2).tan());
  843.     }

  845.     /** {@inheritDoc} */
  846.     @Override
  847.     public T getHyDot() {

  849.         if (!hasDerivatives()) {
  850.             return null;
  851.         }

  853.         // Check for equatorial retrograde orbit
  854.         if (FastMath.abs(i.subtract(i.getPi()).getReal()) < 1.0e-10) {
  855.             return getZero().add(Double.NaN);
  856.         }

  858.         final FieldUnivariateDerivative1<T> iUD    = new FieldUnivariateDerivative1<>(i,    iDot);
  859.         final FieldUnivariateDerivative1<T> raanUD = new FieldUnivariateDerivative1<>(raan, raanDot);
  860.         return raanUD.sin().multiply(iUD.multiply(0.5).tan()).getFirstDerivative();

  862.     }

  864.     /** {@inheritDoc} */
  865.     @Override
  866.     public T getLv() {
  867.         return pa.add(raan).add(getTrueAnomaly());
  868.     }

  870.     /** {@inheritDoc} */
  871.     @Override
  872.     public T getLvDot() {
  873.         return hasDerivatives() ?
  874.                paDot.add(raanDot).add(getTrueAnomalyDot()) :
  875.                null;
  876.     }

  878.     /** {@inheritDoc} */
  879.     @Override
  880.     public T getLE() {
  881.         return pa.add(raan).add(getEccentricAnomaly());
  882.     }

  884.     /** {@inheritDoc} */
  885.     @Override
  886.     public T getLEDot() {
  887.         return hasDerivatives() ?
  888.                paDot.add(raanDot).add(getEccentricAnomalyDot()) :
  889.                null;
  890.     }

  892.     /** {@inheritDoc} */
  893.     @Override
  894.     public T getLM() {
  895.         return pa.add(raan).add(getMeanAnomaly());
  896.     }

  898.     /** {@inheritDoc} */
  899.     @Override
  900.     public T getLMDot() {
  901.         return hasDerivatives() ?
  902.                paDot.add(raanDot).add(getMeanAnomalyDot()) :
  903.                null;
  904.     }

  906.     /** Initialize cached anomaly with rate.
  907.      * @param anomaly input anomaly
  908.      * @param anomalyDot rate of input anomaly
  909.      * @param inputType position angle type passed as input
  910.      * @return anomaly to cache with rate
  911.      * @since 12.1
  912.      */
  913.     private FieldUnivariateDerivative1<T> initializeCachedAnomaly(final T anomaly, final T anomalyDot,
  914.                                                                   final PositionAngleType inputType) {
  915.         if (cachedPositionAngleType == inputType) {
  916.             return new FieldUnivariateDerivative1<>(anomaly, anomalyDot);

  918.         } else {
  919.             final FieldUnivariateDerivative1<T> eUD = new FieldUnivariateDerivative1<>(e, eDot);
  920.             final FieldUnivariateDerivative1<T> anomalyUD = new FieldUnivariateDerivative1<>(anomaly, anomalyDot);

  922.             if (a.getReal() < 0) {
  923.                 switch (cachedPositionAngleType) {
  924.                     case MEAN:
  925.                         if (inputType == PositionAngleType.ECCENTRIC) {
  926.                             return FieldKeplerianAnomalyUtility.hyperbolicEccentricToMean(eUD, anomalyUD);
  927.                         } else {
  928.                             return FieldKeplerianAnomalyUtility.hyperbolicTrueToMean(eUD, anomalyUD);
  929.                         }

  931.                     case ECCENTRIC:
  932.                         if (inputType == PositionAngleType.MEAN) {
  933.                             return FieldKeplerianAnomalyUtility.hyperbolicMeanToEccentric(eUD, anomalyUD);
  934.                         } else {
  935.                             return FieldKeplerianAnomalyUtility.hyperbolicTrueToEccentric(eUD, anomalyUD);
  936.                         }

  938.                     case TRUE:
  939.                         if (inputType == PositionAngleType.MEAN) {
  940.                             return FieldKeplerianAnomalyUtility.hyperbolicMeanToTrue(eUD, anomalyUD);
  941.                         } else {
  942.                             return FieldKeplerianAnomalyUtility.hyperbolicEccentricToTrue(eUD, anomalyUD);
  943.                         }

  945.                     default:
  946.                         break;
  947.                 }

  949.             } else {
  950.                 switch (cachedPositionAngleType) {
  951.                     case MEAN:
  952.                         if (inputType == PositionAngleType.ECCENTRIC) {
  953.                             return FieldKeplerianAnomalyUtility.ellipticEccentricToMean(eUD, anomalyUD);
  954.                         } else {
  955.                             return FieldKeplerianAnomalyUtility.ellipticTrueToMean(eUD, anomalyUD);
  956.                         }

  958.                     case ECCENTRIC:
  959.                         if (inputType == PositionAngleType.MEAN) {
  960.                             return FieldKeplerianAnomalyUtility.ellipticMeanToEccentric(eUD, anomalyUD);
  961.                         } else {
  962.                             return FieldKeplerianAnomalyUtility.ellipticTrueToEccentric(eUD, anomalyUD);
  963.                         }

  965.                     case TRUE:
  966.                         if (inputType == PositionAngleType.MEAN) {
  967.                             return FieldKeplerianAnomalyUtility.ellipticMeanToTrue(eUD, anomalyUD);
  968.                         } else {
  969.                             return FieldKeplerianAnomalyUtility.ellipticEccentricToTrue(eUD, anomalyUD);
  970.                         }

  972.                     default:
  973.                         break;
  974.                 }

  976.             }
  977.             throw new OrekitInternalError(null);
  978.         }

  980.     }

  982.     /** Initialize cached anomaly.
  983.      * @param anomaly input anomaly
  984.      * @param inputType position angle type passed as input
  985.      * @return anomaly to cache
  986.      * @since 12.1
  987.      */
  988.     private T initializeCachedAnomaly(final T anomaly, final PositionAngleType inputType) {
  989.         return FieldKeplerianAnomalyUtility.convertAnomaly(inputType, anomaly, e, cachedPositionAngleType);
  990.     }

  992.     /** Compute reference axes.
  993.      * @return reference axes
  994.      * @since 12.0
  995.      */
  996.     private FieldVector3D<T>[] referenceAxes() {

  998.         // preliminary variables
  999.         final FieldSinCos<T> scRaan = FastMath.sinCos(raan);
  1000.         final FieldSinCos<T> scPa   = FastMath.sinCos(pa);
  1001.         final FieldSinCos<T> scI    = FastMath.sinCos(i);
  1002.         final T cosRaan = scRaan.cos();
  1003.         final T sinRaan = scRaan.sin();
  1004.         final T cosPa   = scPa.cos();
  1005.         final T sinPa   = scPa.sin();
  1006.         final T cosI    = scI.cos();
  1007.         final T sinI    = scI.sin();
  1008.         final T crcp    = cosRaan.multiply(cosPa);
  1009.         final T crsp    = cosRaan.multiply(sinPa);
  1010.         final T srcp    = sinRaan.multiply(cosPa);
  1011.         final T srsp    = sinRaan.multiply(sinPa);

  1013.         // reference axes defining the orbital plane
  1014.         @SuppressWarnings("unchecked")
  1015.         final FieldVector3D<T>[] axes = (FieldVector3D<T>[]) Array.newInstance(FieldVector3D.class, 2);
  1016.         axes[0] = new FieldVector3D<>(crcp.subtract(cosI.multiply(srsp)),  srcp.add(cosI.multiply(crsp)), sinI.multiply(sinPa));
  1017.         axes[1] = new FieldVector3D<>(crsp.add(cosI.multiply(srcp)).negate(), cosI.multiply(crcp).subtract(srsp), sinI.multiply(cosPa));

  1019.         return axes;

  1021.     }

  1023.     /** Compute position and velocity but not acceleration.
  1024.      */
  1025.     private void computePVWithoutA() {

  1027.         if (partialPV != null) {
  1028.             // already computed
  1029.             return;
  1030.         }

  1032.         final FieldVector3D<T>[] axes = referenceAxes();

  1034.         if (isElliptical()) {

  1036.             // elliptical case

  1038.             // elliptic eccentric anomaly
  1039.             final T uME2             = e.negate().add(1).multiply(e.add(1));
  1040.             final T s1Me2            = uME2.sqrt();
  1041.             final FieldSinCos<T> scE = FastMath.sinCos(getEccentricAnomaly());
  1042.             final T cosE             = scE.cos();
  1043.             final T sinE             = scE.sin();

  1045.             // coordinates of position and velocity in the orbital plane
  1046.             final T x      = a.multiply(cosE.subtract(e));
  1047.             final T y      = a.multiply(sinE).multiply(s1Me2);
  1048.             final T factor = FastMath.sqrt(getMu().divide(a)).divide(e.negate().multiply(cosE).add(1));
  1049.             final T xDot   = sinE.negate().multiply(factor);
  1050.             final T yDot   = cosE.multiply(s1Me2).multiply(factor);

  1052.             final FieldVector3D<T> position = new FieldVector3D<>(x, axes[0], y, axes[1]);
  1053.             final FieldVector3D<T> velocity = new FieldVector3D<>(xDot, axes[0], yDot, axes[1]);
  1054.             partialPV = new FieldPVCoordinates<>(position, velocity);

  1056.         } else {

  1058.             // hyperbolic case

  1060.             // compute position and velocity factors
  1061.             final FieldSinCos<T> scV = FastMath.sinCos(getTrueAnomaly());
  1062.             final T sinV             = scV.sin();
  1063.             final T cosV             = scV.cos();
  1064.             final T f                = a.multiply(e.square().negate().add(1));
  1065.             final T posFactor        = f.divide(e.multiply(cosV).add(1));
  1066.             final T velFactor        = FastMath.sqrt(getMu().divide(f));

  1068.             final FieldVector3D<T> position     = new FieldVector3D<>(posFactor.multiply(cosV), axes[0], posFactor.multiply(sinV), axes[1]);
  1069.             final FieldVector3D<T> velocity     = new FieldVector3D<>(velFactor.multiply(sinV).negate(), axes[0], velFactor.multiply(e.add(cosV)), axes[1]);
  1070.             partialPV = new FieldPVCoordinates<>(position, velocity);

  1072.         }

  1074.     }

  1076.     /** Compute non-Keplerian part of the acceleration from first time derivatives.
  1077.      * <p>
  1078.      * This method should be called only when {@link #hasDerivatives()} returns true.
  1079.      * </p>
  1080.      * @return non-Keplerian part of the acceleration
  1081.      */
  1082.     private FieldVector3D<T> nonKeplerianAcceleration() {

  1084.         final T[][] dCdP = MathArrays.buildArray(a.getField(), 6, 6);
  1085.         getJacobianWrtParameters(PositionAngleType.MEAN, dCdP);

  1087.         final T nonKeplerianMeanMotion = getMeanAnomalyDot().subtract(getKeplerianMeanMotion());
  1088.         final T nonKeplerianAx =     dCdP[3][0].multiply(aDot).
  1089.                                  add(dCdP[3][1].multiply(eDot)).
  1090.                                  add(dCdP[3][2].multiply(iDot)).
  1091.                                  add(dCdP[3][3].multiply(paDot)).
  1092.                                  add(dCdP[3][4].multiply(raanDot)).
  1093.                                  add(dCdP[3][5].multiply(nonKeplerianMeanMotion));
  1094.         final T nonKeplerianAy =     dCdP[4][0].multiply(aDot).
  1095.                                  add(dCdP[4][1].multiply(eDot)).
  1096.                                  add(dCdP[4][2].multiply(iDot)).
  1097.                                  add(dCdP[4][3].multiply(paDot)).
  1098.                                  add(dCdP[4][4].multiply(raanDot)).
  1099.                                  add(dCdP[4][5].multiply(nonKeplerianMeanMotion));
  1100.         final T nonKeplerianAz =     dCdP[5][0].multiply(aDot).
  1101.                                  add(dCdP[5][1].multiply(eDot)).
  1102.                                  add(dCdP[5][2].multiply(iDot)).
  1103.                                  add(dCdP[5][3].multiply(paDot)).
  1104.                                  add(dCdP[5][4].multiply(raanDot)).
  1105.                                  add(dCdP[5][5].multiply(nonKeplerianMeanMotion));

  1107.         return new FieldVector3D<>(nonKeplerianAx, nonKeplerianAy, nonKeplerianAz);

  1109.     }

  1111.     /** {@inheritDoc} */
  1112.     @Override
  1113.     protected FieldVector3D<T> initPosition() {
  1114.         final FieldVector3D<T>[] axes = referenceAxes();

  1116.         if (isElliptical()) {

  1118.             // elliptical case

  1120.             // elliptic eccentric anomaly
  1121.             final T uME2             = e.negate().add(1).multiply(e.add(1));
  1122.             final T s1Me2            = uME2.sqrt();
  1123.             final FieldSinCos<T> scE = FastMath.sinCos(getEccentricAnomaly());
  1124.             final T cosE             = scE.cos();
  1125.             final T sinE             = scE.sin();

  1127.             return new FieldVector3D<>(a.multiply(cosE.subtract(e)), axes[0], a.multiply(sinE).multiply(s1Me2), axes[1]);

  1129.         } else {

  1131.             // hyperbolic case

  1133.             // compute position and velocity factors
  1134.             final FieldSinCos<T> scV = FastMath.sinCos(getTrueAnomaly());
  1135.             final T sinV             = scV.sin();
  1136.             final T cosV             = scV.cos();
  1137.             final T f                = a.multiply(e.square().negate().add(1));
  1138.             final T posFactor        = f.divide(e.multiply(cosV).add(1));

  1140.             return new FieldVector3D<>(posFactor.multiply(cosV), axes[0], posFactor.multiply(sinV), axes[1]);

  1142.         }

  1144.     }

  1146.     /** {@inheritDoc} */
  1147.     @Override
  1148.     protected TimeStampedFieldPVCoordinates<T> initPVCoordinates() {

  1150.         // position and velocity
  1151.         computePVWithoutA();

  1153.         // acceleration
  1154.         final T r2 = partialPV.getPosition().getNormSq();
  1155.         final FieldVector3D<T> keplerianAcceleration = new FieldVector3D<>(r2.multiply(FastMath.sqrt(r2)).reciprocal().multiply(getMu().negate()),
  1156.                                                                            partialPV.getPosition());
  1157.         final FieldVector3D<T> acceleration = hasDerivatives() ?
  1158.                                               keplerianAcceleration.add(nonKeplerianAcceleration()) :
  1159.                                               keplerianAcceleration;

  1161.         return new TimeStampedFieldPVCoordinates<>(getDate(), partialPV.getPosition(), partialPV.getVelocity(), acceleration);

  1163.     }

  1165.     /** {@inheritDoc} */
  1166.     @Override
  1167.     public FieldKeplerianOrbit<T> shiftedBy(final double dt) {
  1168.         return shiftedBy(getZero().newInstance(dt));
  1169.     }

  1171.     /** {@inheritDoc} */
  1172.     @Override
  1173.     public FieldKeplerianOrbit<T> shiftedBy(final T dt) {

  1175.         // use Keplerian-only motion
  1176.         final FieldKeplerianOrbit<T> keplerianShifted = new FieldKeplerianOrbit<>(a, e, i, pa, raan,
  1177.                                                                                   getKeplerianMeanMotion().multiply(dt).add(getMeanAnomaly()),
  1178.                                                                                   PositionAngleType.MEAN, cachedPositionAngleType, getFrame(), getDate().shiftedBy(dt), getMu());

  1180.         if (hasDerivatives()) {

  1182.             // extract non-Keplerian acceleration from first time derivatives
  1183.             final FieldVector3D<T> nonKeplerianAcceleration = nonKeplerianAcceleration();

  1185.             // add quadratic effect of non-Keplerian acceleration to Keplerian-only shift
  1186.             keplerianShifted.computePVWithoutA();
  1187.             final FieldVector3D<T> fixedP   = new FieldVector3D<>(getOne(), keplerianShifted.partialPV.getPosition(),
  1188.                                                                   dt.square().multiply(0.5), nonKeplerianAcceleration);
  1189.             final T   fixedR2 = fixedP.getNormSq();
  1190.             final T   fixedR  = fixedR2.sqrt();
  1191.             final FieldVector3D<T> fixedV  = new FieldVector3D<>(getOne(), keplerianShifted.partialPV.getVelocity(),
  1192.                                                                  dt, nonKeplerianAcceleration);
  1193.             final FieldVector3D<T> fixedA  = new FieldVector3D<>(fixedR2.multiply(fixedR).reciprocal().multiply(getMu().negate()),
  1194.                                                                  keplerianShifted.partialPV.getPosition(),
  1195.                                                                  getOne(), nonKeplerianAcceleration);

  1197.             // build a new orbit, taking non-Keplerian acceleration into account
  1198.             return new FieldKeplerianOrbit<>(new TimeStampedFieldPVCoordinates<>(keplerianShifted.getDate(),
  1199.                                                                                  fixedP, fixedV, fixedA),
  1200.                                              keplerianShifted.getFrame(), keplerianShifted.getMu());

  1202.         } else {
  1203.             // Keplerian-only motion is all we can do
  1204.             return keplerianShifted;
  1205.         }

  1207.     }

  1209.     /** {@inheritDoc} */
  1210.     @Override
  1211.     protected T[][] computeJacobianMeanWrtCartesian() {
  1212.         if (isElliptical()) {
  1213.             return computeJacobianMeanWrtCartesianElliptical();
  1214.         } else {
  1215.             return computeJacobianMeanWrtCartesianHyperbolic();
  1216.         }
  1217.     }

  1219.     /** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
  1220.      * <p>
  1221.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  1222.      * respect to Cartesian coordinate j (x for j=0, y for j=1, z for j=2, xDot for j=3,
  1223.      * yDot for j=4, zDot for j=5).
  1224.      * </p>
  1225.      * @return 6x6 Jacobian matrix
  1226.      */
  1227.     private T[][] computeJacobianMeanWrtCartesianElliptical() {

  1229.         final T[][] jacobian = MathArrays.buildArray(getA().getField(), 6, 6);

  1231.         // compute various intermediate parameters
  1232.         computePVWithoutA();
  1233.         final FieldVector3D<T> position = partialPV.getPosition();
  1234.         final FieldVector3D<T> velocity = partialPV.getVelocity();
  1235.         final FieldVector3D<T> momentum = partialPV.getMomentum();
  1236.         final T v2         = velocity.getNormSq();
  1237.         final T r2         = position.getNormSq();
  1238.         final T r          = r2.sqrt();
  1239.         final T r3         = r.multiply(r2);

  1241.         final T px         = position.getX();
  1242.         final T py         = position.getY();
  1243.         final T pz         = position.getZ();
  1244.         final T vx         = velocity.getX();
  1245.         final T vy         = velocity.getY();
  1246.         final T vz         = velocity.getZ();
  1247.         final T mx         = momentum.getX();
  1248.         final T my         = momentum.getY();
  1249.         final T mz         = momentum.getZ();

  1251.         final T mu         = getMu();
  1252.         final T sqrtMuA    = FastMath.sqrt(a.multiply(mu));
  1253.         final T sqrtAoMu   = FastMath.sqrt(a.divide(mu));
  1254.         final T a2         = a.square();
  1255.         final T twoA       = a.multiply(2);
  1256.         final T rOnA       = r.divide(a);

  1258.         final T oMe2       = e.square().negate().add(1);
  1259.         final T epsilon    = oMe2.sqrt();
  1260.         final T sqrtRec    = epsilon.reciprocal();

  1262.         final FieldSinCos<T> scI  = FastMath.sinCos(i);
  1263.         final FieldSinCos<T> scPA = FastMath.sinCos(pa);
  1264.         final T cosI       = scI.cos();
  1265.         final T sinI       = scI.sin();
  1266.         final T cosPA      = scPA.cos();
  1267.         final T sinPA      = scPA.sin();

  1269.         final T pv         = FieldVector3D.dotProduct(position, velocity);
  1270.         final T cosE       = a.subtract(r).divide(a.multiply(e));
  1271.         final T sinE       = pv.divide(e.multiply(sqrtMuA));

  1273.         // da
  1274.         final FieldVector3D<T> vectorAR = new FieldVector3D<>(a2.multiply(2).divide(r3), position);
  1275.         final FieldVector3D<T> vectorARDot = velocity.scalarMultiply(a2.multiply(mu.divide(2.).reciprocal()));
  1276.         fillHalfRow(getOne(), vectorAR,    jacobian[0], 0);
  1277.         fillHalfRow(getOne(), vectorARDot, jacobian[0], 3);

  1279.         // de
  1280.         final T factorER3 = pv.divide(twoA);
  1281.         final FieldVector3D<T> vectorER   = new FieldVector3D<>(cosE.multiply(v2).divide(r.multiply(mu)), position,
  1282.                                                                 sinE.divide(sqrtMuA), velocity,
  1283.                                                                 factorER3.negate().multiply(sinE).divide(sqrtMuA), vectorAR);
  1284.         final FieldVector3D<T> vectorERDot = new FieldVector3D<>(sinE.divide(sqrtMuA), position,
  1285.                                                                  cosE.multiply(mu.divide(2.).reciprocal()).multiply(r), velocity,
  1286.                                                                  factorER3.negate().multiply(sinE).divide(sqrtMuA), vectorARDot);
  1287.         fillHalfRow(getOne(), vectorER,    jacobian[1], 0);
  1288.         fillHalfRow(getOne(), vectorERDot, jacobian[1], 3);

  1290.         // dE / dr (Eccentric anomaly)
  1291.         final T coefE = cosE.divide(e.multiply(sqrtMuA));
  1292.         final FieldVector3D<T>  vectorEAnR =
  1293.             new FieldVector3D<>(sinE.negate().multiply(v2).divide(e.multiply(r).multiply(mu)), position, coefE, velocity,
  1294.                                 factorER3.negate().multiply(coefE), vectorAR);

  1296.         // dE / drDot
  1297.         final FieldVector3D<T>  vectorEAnRDot =
  1298.             new FieldVector3D<>(sinE.multiply(-2).multiply(r).divide(e.multiply(mu)), velocity, coefE, position,
  1299.                                 factorER3.negate().multiply(coefE), vectorARDot);

  1301.         // precomputing some more factors
  1302.         final T s1 = sinE.negate().multiply(pz).divide(r).subtract(cosE.multiply(vz).multiply(sqrtAoMu));
  1303.         final T s2 = cosE.negate().multiply(pz).divide(r3);
  1304.         final T s3 = sinE.multiply(vz).divide(sqrtMuA.multiply(-2));
  1305.         final T t1 = sqrtRec.multiply(cosE.multiply(pz).divide(r).subtract(sinE.multiply(vz).multiply(sqrtAoMu)));
  1306.         final T t2 = sqrtRec.multiply(sinE.negate().multiply(pz).divide(r3));
  1307.         final T t3 = sqrtRec.multiply(cosE.subtract(e)).multiply(vz).divide(sqrtMuA.multiply(2));
  1308.         final T t4 = sqrtRec.multiply(e.multiply(sinI).multiply(cosPA).multiply(sqrtRec).subtract(vz.multiply(sqrtAoMu)));
  1309.         final FieldVector3D<T> s = new FieldVector3D<>(cosE.divide(r), this.PLUS_K,
  1310.                                                        s1,       vectorEAnR,
  1311.                                                        s2,       position,
  1312.                                                        s3,       vectorAR);
  1313.         final FieldVector3D<T> sDot = new FieldVector3D<>(sinE.negate().multiply(sqrtAoMu), this.PLUS_K,
  1314.                                                           s1,               vectorEAnRDot,
  1315.                                                           s3,               vectorARDot);
  1316.         final FieldVector3D<T> t =
  1317.             new FieldVector3D<>(sqrtRec.multiply(sinE).divide(r), this.PLUS_K).add(new FieldVector3D<>(t1, vectorEAnR,
  1318.                                                                                                        t2, position,
  1319.                                                                                                        t3, vectorAR,
  1320.                                                                                                        t4, vectorER));
  1321.         final FieldVector3D<T> tDot = new FieldVector3D<>(sqrtRec.multiply(cosE.subtract(e)).multiply(sqrtAoMu), this.PLUS_K,
  1322.                                                           t1,                                                    vectorEAnRDot,
  1323.                                                           t3,                                                    vectorARDot,
  1324.                                                           t4,                                                    vectorERDot);

  1326.         // di
  1327.         final T factorI1 = sinI.negate().multiply(sqrtRec).divide(sqrtMuA);
  1328.         final T i1 =  factorI1;
  1329.         final T i2 =  factorI1.negate().multiply(mz).divide(twoA);
  1330.         final T i3 =  factorI1.multiply(mz).multiply(e).divide(oMe2);
  1331.         final T i4 = cosI.multiply(sinPA);
  1332.         final T i5 = cosI.multiply(cosPA);
  1333.         fillHalfRow(i1, new FieldVector3D<>(vy, vx.negate(), getZero()), i2, vectorAR, i3, vectorER, i4, s, i5, t,
  1334.                     jacobian[2], 0);
  1335.         fillHalfRow(i1, new FieldVector3D<>(py.negate(), px, getZero()), i2, vectorARDot, i3, vectorERDot, i4, sDot, i5, tDot,
  1336.                     jacobian[2], 3);

  1338.         // dpa
  1339.         fillHalfRow(cosPA.divide(sinI), s,    sinPA.negate().divide(sinI), t,    jacobian[3], 0);
  1340.         fillHalfRow(cosPA.divide(sinI), sDot, sinPA.negate().divide(sinI), tDot, jacobian[3], 3);

  1342.         // dRaan
  1343.         final T factorRaanR = (a.multiply(mu).multiply(oMe2).multiply(sinI).multiply(sinI)).reciprocal();
  1344.         fillHalfRow( factorRaanR.negate().multiply(my), new FieldVector3D<>(getZero(), vz, vy.negate()),
  1345.                      factorRaanR.multiply(mx), new FieldVector3D<>(vz.negate(), getZero(),  vx),
  1346.                      jacobian[4], 0);
  1347.         fillHalfRow(factorRaanR.negate().multiply(my), new FieldVector3D<>(getZero(), pz.negate(),  py),
  1348.                      factorRaanR.multiply(mx), new FieldVector3D<>(pz, getZero(), px.negate()),
  1349.                      jacobian[4], 3);

  1351.         // dM
  1352.         fillHalfRow(rOnA, vectorEAnR,    sinE.negate(), vectorER,    jacobian[5], 0);
  1353.         fillHalfRow(rOnA, vectorEAnRDot, sinE.negate(), vectorERDot, jacobian[5], 3);

  1355.         return jacobian;

  1357.     }

  1359.     /** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
  1360.      * <p>
  1361.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  1362.      * respect to Cartesian coordinate j (x for j=0, y for j=1, z for j=2, xDot for j=3,
  1363.      * yDot for j=4, zDot for j=5).
  1364.      * </p>
  1365.      * @return 6x6 Jacobian matrix
  1366.      */
  1367.     private T[][] computeJacobianMeanWrtCartesianHyperbolic() {

  1369.         final T[][] jacobian = MathArrays.buildArray(getA().getField(), 6, 6);

  1371.         // compute various intermediate parameters
  1372.         computePVWithoutA();
  1373.         final FieldVector3D<T> position = partialPV.getPosition();
  1374.         final FieldVector3D<T> velocity = partialPV.getVelocity();
  1375.         final FieldVector3D<T> momentum = partialPV.getMomentum();
  1376.         final T r2         = position.getNormSq();
  1377.         final T r          = r2.sqrt();
  1378.         final T r3         = r.multiply(r2);

  1380.         final T x          = position.getX();
  1381.         final T y          = position.getY();
  1382.         final T z          = position.getZ();
  1383.         final T vx         = velocity.getX();
  1384.         final T vy         = velocity.getY();
  1385.         final T vz         = velocity.getZ();
  1386.         final T mx         = momentum.getX();
  1387.         final T my         = momentum.getY();
  1388.         final T mz         = momentum.getZ();

  1390.         final T mu         = getMu();
  1391.         final T absA       = a.negate();
  1392.         final T sqrtMuA    = absA.multiply(mu).sqrt();
  1393.         final T a2         = a.square();
  1394.         final T rOa        = r.divide(absA);

  1396.         final FieldSinCos<T> scI = FastMath.sinCos(i);
  1397.         final T cosI       = scI.cos();
  1398.         final T sinI       = scI.sin();

  1400.         final T pv         = FieldVector3D.dotProduct(position, velocity);

  1402.         // da
  1403.         final FieldVector3D<T> vectorAR = new FieldVector3D<>(a2.multiply(-2).divide(r3), position);
  1404.         final FieldVector3D<T> vectorARDot = velocity.scalarMultiply(a2.multiply(-2).divide(mu));
  1405.         fillHalfRow(getOne().negate(), vectorAR,    jacobian[0], 0);
  1406.         fillHalfRow(getOne().negate(), vectorARDot, jacobian[0], 3);

  1408.         // differentials of the momentum
  1409.         final T m      = momentum.getNorm();
  1410.         final T oOm    = m.reciprocal();
  1411.         final FieldVector3D<T> dcXP = new FieldVector3D<>(getZero(), vz, vy.negate());
  1412.         final FieldVector3D<T> dcYP = new FieldVector3D<>(vz.negate(),   getZero(),  vx);
  1413.         final FieldVector3D<T> dcZP = new FieldVector3D<>( vy, vx.negate(),   getZero());
  1414.         final FieldVector3D<T> dcXV = new FieldVector3D<>(  getZero(),  z.negate(),   y);
  1415.         final FieldVector3D<T> dcYV = new FieldVector3D<>(  z,   getZero(),  x.negate());
  1416.         final FieldVector3D<T> dcZV = new FieldVector3D<>( y.negate(),   x,   getZero());
  1417.         final FieldVector3D<T> dCP  = new FieldVector3D<>(mx.multiply(oOm), dcXP, my.multiply(oOm), dcYP, mz.multiply(oOm), dcZP);
  1418.         final FieldVector3D<T> dCV  = new FieldVector3D<>(mx.multiply(oOm), dcXV, my.multiply(oOm), dcYV, mz.multiply(oOm), dcZV);

  1420.         // dp
  1421.         final T mOMu   = m.divide(mu);
  1422.         final FieldVector3D<T> dpP  = new FieldVector3D<>(mOMu.multiply(2), dCP);
  1423.         final FieldVector3D<T> dpV  = new FieldVector3D<>(mOMu.multiply(2), dCV);

  1425.         // de
  1426.         final T p      = m.multiply(mOMu);
  1427.         final T moO2ae = absA.multiply(2).multiply(e).reciprocal();
  1428.         final T m2OaMu = p.negate().divide(absA);
  1429.         fillHalfRow(moO2ae, dpP, m2OaMu.multiply(moO2ae), vectorAR,    jacobian[1], 0);
  1430.         fillHalfRow(moO2ae, dpV, m2OaMu.multiply(moO2ae), vectorARDot, jacobian[1], 3);

  1432.         // di
  1433.         final T cI1 = m.multiply(sinI).reciprocal();
  1434.         final T cI2 = cosI.multiply(cI1);
  1435.         fillHalfRow(cI2, dCP, cI1.negate(), dcZP, jacobian[2], 0);
  1436.         fillHalfRow(cI2, dCV, cI1.negate(), dcZV, jacobian[2], 3);


  1439.         // dPA
  1440.         final T cP1     =  y.multiply(oOm);
  1441.         final T cP2     =  x.negate().multiply(oOm);
  1442.         final T cP3     =  mx.multiply(cP1).add(my.multiply(cP2)).negate();
  1443.         final T cP4     =  cP3.multiply(oOm);
  1444.         final T cP5     =  r2.multiply(sinI).multiply(sinI).negate().reciprocal();
  1445.         final T cP6     = z.multiply(cP5);
  1446.         final T cP7     = cP3.multiply(cP5);
  1447.         final FieldVector3D<T> dacP  = new FieldVector3D<>(cP1, dcXP, cP2, dcYP, cP4, dCP, oOm, new FieldVector3D<>(my.negate(), mx, getZero()));
  1448.         final FieldVector3D<T> dacV  = new FieldVector3D<>(cP1, dcXV, cP2, dcYV, cP4, dCV);
  1449.         final FieldVector3D<T> dpoP  = new FieldVector3D<>(cP6, dacP, cP7, this.PLUS_K);
  1450.         final FieldVector3D<T> dpoV  = new FieldVector3D<>(cP6, dacV);

  1452.         final T re2     = r2.multiply(e.square());
  1453.         final T recOre2 = p.subtract(r).divide(re2);
  1454.         final T resOre2 = pv.multiply(mOMu).divide(re2);
  1455.         final FieldVector3D<T> dreP  = new FieldVector3D<>(mOMu, velocity, pv.divide(mu), dCP);
  1456.         final FieldVector3D<T> dreV  = new FieldVector3D<>(mOMu, position, pv.divide(mu), dCV);
  1457.         final FieldVector3D<T> davP  = new FieldVector3D<>(resOre2.negate(), dpP, recOre2, dreP, resOre2.divide(r), position);
  1458.         final FieldVector3D<T> davV  = new FieldVector3D<>(resOre2.negate(), dpV, recOre2, dreV);
  1459.         fillHalfRow(getOne(), dpoP, getOne().negate(), davP, jacobian[3], 0);
  1460.         fillHalfRow(getOne(), dpoV, getOne().negate(), davV, jacobian[3], 3);

  1462.         // dRAAN
  1463.         final T cO0 = cI1.square();
  1464.         final T cO1 =  mx.multiply(cO0);
  1465.         final T cO2 =  my.negate().multiply(cO0);
  1466.         fillHalfRow(cO1, dcYP, cO2, dcXP, jacobian[4], 0);
  1467.         fillHalfRow(cO1, dcYV, cO2, dcXV, jacobian[4], 3);

  1469.         // dM
  1470.         final T s2a    = pv.divide(absA.multiply(2));
  1471.         final T oObux  = m.square().add(absA.multiply(mu)).sqrt().reciprocal();
  1472.         final T scasbu = pv.multiply(oObux);
  1473.         final FieldVector3D<T> dauP = new FieldVector3D<>(sqrtMuA.reciprocal(), velocity, s2a.negate().divide(sqrtMuA), vectorAR);
  1474.         final FieldVector3D<T> dauV = new FieldVector3D<>(sqrtMuA.reciprocal(), position, s2a.negate().divide(sqrtMuA), vectorARDot);
  1475.         final FieldVector3D<T> dbuP = new FieldVector3D<>(oObux.multiply(mu.divide(2.)), vectorAR,    m.multiply(oObux), dCP);
  1476.         final FieldVector3D<T> dbuV = new FieldVector3D<>(oObux.multiply(mu.divide(2.)), vectorARDot, m.multiply(oObux), dCV);
  1477.         final FieldVector3D<T> dcuP = new FieldVector3D<>(oObux, velocity, scasbu.negate().multiply(oObux), dbuP);
  1478.         final FieldVector3D<T> dcuV = new FieldVector3D<>(oObux, position, scasbu.negate().multiply(oObux), dbuV);
  1479.         fillHalfRow(getOne(), dauP, e.negate().divide(rOa.add(1)), dcuP, jacobian[5], 0);
  1480.         fillHalfRow(getOne(), dauV, e.negate().divide(rOa.add(1)), dcuV, jacobian[5], 3);

  1482.         return jacobian;

  1484.     }

  1486.     /** {@inheritDoc} */
  1487.     @Override
  1488.     protected T[][] computeJacobianEccentricWrtCartesian() {
  1489.         if (isElliptical()) {
  1490.             return computeJacobianEccentricWrtCartesianElliptical();
  1491.         } else {
  1492.             return computeJacobianEccentricWrtCartesianHyperbolic();
  1493.         }
  1494.     }

  1496.     /** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
  1497.      * <p>
  1498.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  1499.      * respect to Cartesian coordinate j (x for j=0, y for j=1, z for j=2, xDot for j=3,
  1500.      * yDot for j=4, zDot for j=5).
  1501.      * </p>
  1502.      * @return 6x6 Jacobian matrix
  1503.      */
  1504.     private T[][] computeJacobianEccentricWrtCartesianElliptical() {

  1506.         // start by computing the Jacobian with mean angle
  1507.         final T[][] jacobian = computeJacobianMeanWrtCartesianElliptical();

  1509.         // Differentiating the Kepler equation M = E - e sin E leads to:
  1510.         // dM = (1 - e cos E) dE - sin E de
  1511.         // which is inverted and rewritten as:
  1512.         // dE = a/r dM + sin E a/r de
  1513.         final FieldSinCos<T> scE = FastMath.sinCos(getEccentricAnomaly());
  1514.         final T aOr              = e.negate().multiply(scE.cos()).add(1).reciprocal();

  1516.         // update anomaly row
  1517.         final T[] eRow           = jacobian[1];
  1518.         final T[] anomalyRow     = jacobian[5];
  1519.         for (int j = 0; j < anomalyRow.length; ++j) {
  1520.             anomalyRow[j] = aOr.multiply(anomalyRow[j].add(scE.sin().multiply(eRow[j])));
  1521.         }

  1523.         return jacobian;

  1525.     }

  1527.     /** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
  1528.      * <p>
  1529.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  1530.      * respect to Cartesian coordinate j (x for j=0, y for j=1, z for j=2, xDot for j=3,
  1531.      * yDot for j=4, zDot for j=5).
  1532.      * </p>
  1533.      * @return 6x6 Jacobian matrix
  1534.      */
  1535.     private T[][] computeJacobianEccentricWrtCartesianHyperbolic() {

  1537.         // start by computing the Jacobian with mean angle
  1538.         final T[][] jacobian = computeJacobianMeanWrtCartesianHyperbolic();

  1540.         // Differentiating the Kepler equation M = e sinh H - H leads to:
  1541.         // dM = (e cosh H - 1) dH + sinh H de
  1542.         // which is inverted and rewritten as:
  1543.         // dH = 1 / (e cosh H - 1) dM - sinh H / (e cosh H - 1) de
  1544.         final T H      = getEccentricAnomaly();
  1545.         final T coshH  = H.cosh();
  1546.         final T sinhH  = H.sinh();
  1547.         final T absaOr = e.multiply(coshH).subtract(1).reciprocal();
  1548.         // update anomaly row
  1549.         final T[] eRow       = jacobian[1];
  1550.         final T[] anomalyRow = jacobian[5];

  1552.         for (int j = 0; j < anomalyRow.length; ++j) {
  1553.             anomalyRow[j] = absaOr.multiply(anomalyRow[j].subtract(sinhH.multiply(eRow[j])));

  1555.         }

  1557.         return jacobian;

  1559.     }

  1561.     /** {@inheritDoc} */
  1562.     @Override
  1563.     protected T[][] computeJacobianTrueWrtCartesian() {
  1564.         if (isElliptical()) {
  1565.             return computeJacobianTrueWrtCartesianElliptical();
  1566.         } else {
  1567.             return computeJacobianTrueWrtCartesianHyperbolic();
  1568.         }
  1569.     }

  1571.     /** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
  1572.      * <p>
  1573.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  1574.      * respect to Cartesian coordinate j (x for j=0, y for j=1, z for j=2, xDot for j=3,
  1575.      * yDot for j=4, zDot for j=5).
  1576.      * </p>
  1577.      * @return 6x6 Jacobian matrix
  1578.      */
  1579.     private T[][] computeJacobianTrueWrtCartesianElliptical() {

  1581.         // start by computing the Jacobian with eccentric angle
  1582.         final T[][] jacobian = computeJacobianEccentricWrtCartesianElliptical();
  1583.         // Differentiating the eccentric anomaly equation sin E = sqrt(1-e^2) sin v / (1 + e cos v)
  1584.         // and using cos E = (e + cos v) / (1 + e cos v) to get rid of cos E leads to:
  1585.         // dE = [sqrt (1 - e^2) / (1 + e cos v)] dv - [sin E / (1 - e^2)] de
  1586.         // which is inverted and rewritten as:
  1587.         // dv = sqrt (1 - e^2) a/r dE + [sin E / sqrt (1 - e^2)] a/r de
  1588.         final T e2               = e.square();
  1589.         final T oMe2             = e2.negate().add(1);
  1590.         final T epsilon          = oMe2.sqrt();
  1591.         final FieldSinCos<T> scE = FastMath.sinCos(getEccentricAnomaly());
  1592.         final T aOr              = e.multiply(scE.cos()).negate().add(1).reciprocal();
  1593.         final T aFactor          = epsilon.multiply(aOr);
  1594.         final T eFactor          = scE.sin().multiply(aOr).divide(epsilon);

  1596.         // update anomaly row
  1597.         final T[] eRow           = jacobian[1];
  1598.         final T[] anomalyRow     = jacobian[5];
  1599.         for (int j = 0; j < anomalyRow.length; ++j) {
  1600.             anomalyRow[j] = aFactor.multiply(anomalyRow[j]).add(eFactor.multiply(eRow[j]));
  1601.         }
  1602.         return jacobian;

  1604.     }

  1606.     /** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
  1607.      * <p>
  1608.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  1609.      * respect to Cartesian coordinate j (x for j=0, y for j=1, z for j=2, xDot for j=3,
  1610.      * yDot for j=4, zDot for j=5).
  1611.      * </p>
  1612.      * @return 6x6 Jacobian matrix
  1613.      */
  1614.     private T[][] computeJacobianTrueWrtCartesianHyperbolic() {

  1616.         // start by computing the Jacobian with eccentric angle
  1617.         final T[][] jacobian = computeJacobianEccentricWrtCartesianHyperbolic();

  1619.         // Differentiating the eccentric anomaly equation sinh H = sqrt(e^2-1) sin v / (1 + e cos v)
  1620.         // and using cosh H = (e + cos v) / (1 + e cos v) to get rid of cosh H leads to:
  1621.         // dH = [sqrt (e^2 - 1) / (1 + e cos v)] dv + [sinh H / (e^2 - 1)] de
  1622.         // which is inverted and rewritten as:
  1623.         // dv = sqrt (1 - e^2) a/r dH - [sinh H / sqrt (e^2 - 1)] a/r de
  1624.         final T e2       = e.square();
  1625.         final T e2Mo     = e2.subtract(1);
  1626.         final T epsilon  = e2Mo.sqrt();
  1627.         final T H        = getEccentricAnomaly();
  1628.         final T coshH    = H.cosh();
  1629.         final T sinhH    = H.sinh();
  1630.         final T aOr      = e.multiply(coshH).subtract(1).reciprocal();
  1631.         final T aFactor  = epsilon.multiply(aOr);
  1632.         final T eFactor  = sinhH.multiply(aOr).divide(epsilon);

  1634.         // update anomaly row
  1635.         final T[] eRow           = jacobian[1];
  1636.         final T[] anomalyRow     = jacobian[5];
  1637.         for (int j = 0; j < anomalyRow.length; ++j) {
  1638.             anomalyRow[j] = aFactor.multiply(anomalyRow[j]).subtract(eFactor.multiply(eRow[j]));
  1639.         }

  1641.         return jacobian;

  1643.     }

  1645.     /** {@inheritDoc} */
  1646.     @Override
  1647.     public void addKeplerContribution(final PositionAngleType type, final T gm,
  1648.                                       final T[] pDot) {
  1649.         pDot[5] = pDot[5].add(computeKeplerianAnomalyDot(type, a, e, gm, cachedAnomaly, cachedPositionAngleType));
  1650.     }

  1652.     /**
  1653.      * Compute rate of argument of latitude.
  1654.      * @param type position angle type of rate
  1655.      * @param a semi major axis
  1656.      * @param e eccentricity
  1657.      * @param mu mu
  1658.      * @param anomaly anomaly
  1659.      * @param cachedType position angle type of passed anomaly
  1660.      * @param <T> field type
  1661.      * @return first-order time derivative for anomaly
  1662.      * @since 12.2
  1663.      */
  1664.     private static <T extends CalculusFieldElement<T>> T computeKeplerianAnomalyDot(final PositionAngleType type, final T a, final T e,
  1665.                                                                                     final T mu, final T anomaly, final PositionAngleType cachedType) {
  1666.         final T absA = a.abs();
  1667.         final T n    = absA.reciprocal().multiply(mu).sqrt().divide(absA);
  1668.         if (type == PositionAngleType.MEAN) {
  1669.             return n;
  1670.         }
  1671.         final T ksi;
  1672.         final T oMe2;
  1673.         final T trueAnomaly = FieldKeplerianAnomalyUtility.convertAnomaly(cachedType, anomaly, e, PositionAngleType.TRUE);
  1674.         if (type == PositionAngleType.ECCENTRIC) {
  1675.             oMe2 = e.square().negate().add(1).abs();
  1676.             ksi = e.multiply(trueAnomaly.cos()).add(1);
  1677.             return n.multiply(ksi).divide(oMe2);
  1678.         } else {
  1679.             oMe2 = e.square().negate().add(1).abs();
  1680.             ksi  = e.multiply(trueAnomaly.cos()).add(1);
  1681.             return n.multiply(ksi).multiply(ksi).divide(oMe2.multiply(oMe2.sqrt()));
  1682.         }
  1683.     }

  1685.     /**  Returns a string representation of this Keplerian parameters object.
  1686.      * @return a string representation of this object
  1687.      */
  1688.     public String toString() {
  1689.         return new StringBuilder().append("Keplerian parameters: ").append('{').
  1690.                                   append("a: ").append(a.getReal()).
  1691.                                   append("; e: ").append(e.getReal()).
  1692.                                   append("; i: ").append(FastMath.toDegrees(i.getReal())).
  1693.                                   append("; pa: ").append(FastMath.toDegrees(pa.getReal())).
  1694.                                   append("; raan: ").append(FastMath.toDegrees(raan.getReal())).
  1695.                                   append("; v: ").append(FastMath.toDegrees(getTrueAnomaly().getReal())).
  1696.                                   append(";}").toString();
  1697.     }

  1699.     /** {@inheritDoc} */
  1700.     @Override
  1701.     public PositionAngleType getCachedPositionAngleType() {
  1702.         return cachedPositionAngleType;
  1703.     }

  1705.     /** {@inheritDoc} */
  1706.     @Override
  1707.     public boolean hasRates() {
  1708.         return hasDerivatives();
  1709.     }

  1711.     /** {@inheritDoc} */
  1712.     @Override
  1713.     public FieldKeplerianOrbit<T> removeRates() {
  1714.         return new FieldKeplerianOrbit<>(getA(), getE(), getI(), getPerigeeArgument(), getRightAscensionOfAscendingNode(),
  1715.                 cachedAnomaly, cachedPositionAngleType, getFrame(), getDate(), getMu());
  1716.     }

  1718.     /** Check if the given parameter is within an acceptable range.
  1719.      * The bounds are inclusive: an exception is raised when either of those conditions are met:
  1720.      * <ul>
  1721.      *     <li>The parameter is strictly greater than upperBound</li>
  1722.      *     <li>The parameter is strictly lower than lowerBound</li>
  1723.      * </ul>
  1724.      * <p>
  1725.      * In either of these cases, an OrekitException is raised.
  1726.      * </p>
  1727.      * @param parameterName name of the parameter
  1728.      * @param parameter value of the parameter
  1729.      * @param lowerBound lower bound of the acceptable range (inclusive)
  1730.      * @param upperBound upper bound of the acceptable range (inclusive)
  1731.      */
  1732.     private void checkParameterRangeInclusive(final String parameterName, final double parameter,
  1733.                                               final double lowerBound, final double upperBound) {
  1734.         if (parameter < lowerBound || parameter > upperBound) {
  1735.             throw new OrekitException(OrekitMessages.INVALID_PARAMETER_RANGE, parameterName,
  1736.                                       parameter, lowerBound, upperBound);
  1737.         }
  1738.     }

  1740.     /** {@inheritDoc} */
  1741.     @Override
  1742.     public KeplerianOrbit toOrbit() {
  1743.         final double cachedPositionAngle = cachedAnomaly.getReal();
  1744.         if (hasDerivatives()) {
  1745.             return new KeplerianOrbit(a.getReal(), e.getReal(), i.getReal(),
  1746.                                       pa.getReal(), raan.getReal(), cachedPositionAngle,
  1747.                                       aDot.getReal(), eDot.getReal(), iDot.getReal(),
  1748.                                       paDot.getReal(), raanDot.getReal(),
  1749.                                       cachedAnomalyDot.getReal(),
  1750.                                       cachedPositionAngleType, cachedPositionAngleType,
  1751.                                       getFrame(), getDate().toAbsoluteDate(), getMu().getReal());
  1752.         } else {
  1753.             return new KeplerianOrbit(a.getReal(), e.getReal(), i.getReal(),
  1754.                                       pa.getReal(), raan.getReal(), cachedPositionAngle,
  1755.                                       cachedPositionAngleType, cachedPositionAngleType,
  1756.                                       getFrame(), getDate().toAbsoluteDate(), getMu().getReal());
  1757.         }
  1758.     }


  1761. }
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