FieldOrbit.java

  1. /* Copyright 2002-2022 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;



  21. import org.hipparchus.CalculusFieldElement;
  22. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  23. import org.hipparchus.linear.FieldDecompositionSolver;
  24. import org.hipparchus.linear.FieldLUDecomposition;
  25. import org.hipparchus.linear.FieldMatrix;
  26. import org.hipparchus.linear.MatrixUtils;
  27. import org.hipparchus.util.MathArrays;
  28. import org.orekit.errors.OrekitIllegalArgumentException;
  29. import org.orekit.errors.OrekitInternalError;
  30. import org.orekit.errors.OrekitMessages;
  31. import org.orekit.frames.Frame;
  32. import org.orekit.frames.Transform;
  33. import org.orekit.time.FieldAbsoluteDate;
  34. import org.orekit.time.FieldTimeInterpolable;
  35. import org.orekit.time.FieldTimeShiftable;
  36. import org.orekit.time.FieldTimeStamped;
  37. import org.orekit.utils.FieldPVCoordinates;
  38. import org.orekit.utils.FieldPVCoordinatesProvider;
  39. import org.orekit.utils.TimeStampedFieldPVCoordinates;
  40. import org.orekit.utils.TimeStampedPVCoordinates;

  42. /**
  43.  * This class handles orbital parameters.

  45.  * <p>
  46.  * For user convenience, both the Cartesian and the equinoctial elements
  47.  * are provided by this class, regardless of the canonical representation
  48.  * implemented in the derived class (which may be classical Keplerian
  49.  * elements for example).
  50.  * </p>
  51.  * <p>
  52.  * The parameters are defined in a frame specified by the user. It is important
  53.  * to make sure this frame is consistent: it probably is inertial and centered
  54.  * on the central body. This information is used for example by some
  55.  * force models.
  56.  * </p>
  57.  * <p>
  58.  * Instance of this class are guaranteed to be immutable.
  59.  * </p>
  60.  * @author Luc Maisonobe
  61.  * @author Guylaine Prat
  62.  * @author Fabien Maussion
  63.  * @author V&eacute;ronique Pommier-Maurussane
  64.  * @since 9.0
  65.  */
  66. public abstract class FieldOrbit<T extends CalculusFieldElement<T>>
  67.     implements FieldPVCoordinatesProvider<T>, FieldTimeStamped<T>, FieldTimeShiftable<FieldOrbit<T>, T>, FieldTimeInterpolable<FieldOrbit<T>, T> {

  69.     /** Frame in which are defined the orbital parameters. */
  70.     private final Frame frame;

  72.     /** Date of the orbital parameters. */
  73.     private final FieldAbsoluteDate<T> date;

  75.     /** Value of mu used to compute position and velocity (m³/s²). */
  76.     private final T mu;

  78.     /** Computed PVCoordinates. */
  79.     private transient TimeStampedFieldPVCoordinates<T> pvCoordinates;

  81.     /** Jacobian of the orbital parameters with mean angle with respect to the Cartesian coordinates. */
  82.     private transient T[][] jacobianMeanWrtCartesian;

  84.     /** Jacobian of the Cartesian coordinates with respect to the orbital parameters with mean angle. */
  85.     private transient T[][] jacobianWrtParametersMean;

  87.     /** Jacobian of the orbital parameters with eccentric angle with respect to the Cartesian coordinates. */
  88.     private transient T[][] jacobianEccentricWrtCartesian;

  90.     /** Jacobian of the Cartesian coordinates with respect to the orbital parameters with eccentric angle. */
  91.     private transient T[][] jacobianWrtParametersEccentric;

  93.     /** Jacobian of the orbital parameters with true angle with respect to the Cartesian coordinates. */
  94.     private transient T[][] jacobianTrueWrtCartesian;

  96.     /** Jacobian of the Cartesian coordinates with respect to the orbital parameters with true angle. */
  97.     private transient T[][] jacobianWrtParametersTrue;

  99.     /** Default constructor.
  100.      * Build a new instance with arbitrary default elements.
  101.      * @param frame the frame in which the parameters are defined
  102.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  103.      * @param date date of the orbital parameters
  104.      * @param mu central attraction coefficient (m^3/s^2)
  105.      * @exception IllegalArgumentException if frame is not a {@link
  106.      * Frame#isPseudoInertial pseudo-inertial frame}
  107.      */
  108.     protected FieldOrbit(final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
  109.         throws IllegalArgumentException {
  110.         ensurePseudoInertialFrame(frame);
  111.         this.date                      = date;
  112.         this.mu                        = mu;
  113.         this.pvCoordinates             = null;
  114.         this.frame                     = frame;
  115.         jacobianMeanWrtCartesian       = null;
  116.         jacobianWrtParametersMean      = null;
  117.         jacobianEccentricWrtCartesian  = null;
  118.         jacobianWrtParametersEccentric = null;
  119.         jacobianTrueWrtCartesian       = null;
  120.         jacobianWrtParametersTrue      = null;
  121.     }

  123.     /** Set the orbit from Cartesian parameters.
  124.      *
  125.      * <p> The acceleration provided in {@code FieldPVCoordinates} is accessible using
  126.      * {@link #getPVCoordinates()} and {@link #getPVCoordinates(Frame)}. All other methods
  127.      * use {@code mu} and the position to compute the acceleration, including
  128.      * {@link #shiftedBy(CalculusFieldElement)} and {@link #getPVCoordinates(FieldAbsoluteDate, Frame)}.
  129.      *
  130.      * @param FieldPVCoordinates the position and velocity in the inertial frame
  131.      * @param frame the frame in which the {@link TimeStampedPVCoordinates} are defined
  132.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  133.      * @param mu central attraction coefficient (m^3/s^2)
  134.      * @exception IllegalArgumentException if frame is not a {@link
  135.      * Frame#isPseudoInertial pseudo-inertial frame}
  136.      */
  137.     protected FieldOrbit(final TimeStampedFieldPVCoordinates<T> FieldPVCoordinates, final Frame frame, final T mu)
  138.         throws IllegalArgumentException {
  139.         ensurePseudoInertialFrame(frame);
  140.         this.date = FieldPVCoordinates.getDate();
  141.         this.mu = mu;
  142.         if (FieldPVCoordinates.getAcceleration().getNormSq().getReal() == 0.0) {
  143.             // the acceleration was not provided,
  144.             // compute it from Newtonian attraction
  145.             final T r2 = FieldPVCoordinates.getPosition().getNormSq();
  146.             final T r3 = r2.multiply(r2.sqrt());
  147.             this.pvCoordinates = new TimeStampedFieldPVCoordinates<>(FieldPVCoordinates.getDate(),
  148.                                                                      FieldPVCoordinates.getPosition(),
  149.                                                                      FieldPVCoordinates.getVelocity(),
  150.                                                                      new FieldVector3D<>(r3.reciprocal().multiply(mu.negate()), FieldPVCoordinates.getPosition()));
  151.         } else {
  152.             this.pvCoordinates = FieldPVCoordinates;
  153.         }
  154.         this.frame = frame;
  155.     }

  157.     /** Check if Cartesian coordinates include non-Keplerian acceleration.
  158.      * @param pva Cartesian coordinates
  159.      * @param mu central attraction coefficient
  160.      * @param <T> type of the field elements
  161.      * @return true if Cartesian coordinates include non-Keplerian acceleration
  162.      */
  163.     protected static <T extends CalculusFieldElement<T>> boolean hasNonKeplerianAcceleration(final FieldPVCoordinates<T> pva, final T mu) {

  165.         final FieldVector3D<T> a = pva.getAcceleration();
  166.         if (a == null) {
  167.             return false;
  168.         }

  170.         final FieldVector3D<T> p = pva.getPosition();
  171.         final T r2 = p.getNormSq();
  172.         final T r  = r2.sqrt();
  173.         final FieldVector3D<T> keplerianAcceleration = new FieldVector3D<>(r.multiply(r2).reciprocal().multiply(mu.negate()), p);
  174.         if (a.getNorm().getReal() > 1.0e-9 * keplerianAcceleration.getNorm().getReal()) {
  175.             // we have a relevant acceleration, we can compute derivatives
  176.             return true;
  177.         } else {
  178.             // the provided acceleration is either too small to be reliable (probably even 0), or NaN
  179.             return false;
  180.         }

  182.     }

  184.     /** Get the orbit type.
  185.      * @return orbit type
  186.      */
  187.     public abstract OrbitType getType();

  189.     /** Ensure the defining frame is a pseudo-inertial frame.
  190.      * @param frame frame to check
  191.      * @exception IllegalArgumentException if frame is not a {@link
  192.      * Frame#isPseudoInertial pseudo-inertial frame}
  193.      */
  194.     private static void ensurePseudoInertialFrame(final Frame frame)
  195.         throws IllegalArgumentException {
  196.         if (!frame.isPseudoInertial()) {
  197.             throw new OrekitIllegalArgumentException(OrekitMessages.NON_PSEUDO_INERTIAL_FRAME,
  198.                                                      frame.getName());
  199.         }
  200.     }

  202.     /** Get the frame in which the orbital parameters are defined.
  203.      * @return frame in which the orbital parameters are defined
  204.      */
  205.     public Frame getFrame() {
  206.         return frame;
  207.     }

  209.     /**Transforms the FieldOrbit instance into an Orbit instance.
  210.      * @return Orbit instance with same properties
  211.      */
  212.     public abstract Orbit toOrbit();

  214.     /** Get the semi-major axis.
  215.      * <p>Note that the semi-major axis is considered negative for hyperbolic orbits.</p>
  216.      * @return semi-major axis (m)
  217.      */
  218.     public abstract T getA();

  220.     /** Get the semi-major axis derivative.
  221.      * <p>Note that the semi-major axis is considered negative for hyperbolic orbits.</p>
  222.      * <p>
  223.      * If the orbit was created without derivatives, the value returned is null.
  224.      * </p>
  225.      * @return semi-major axis  derivative (m/s)
  226.      */
  227.     public abstract T getADot();

  229.     /** Get the first component of the equinoctial eccentricity vector.
  230.      * @return first component of the equinoctial eccentricity vector
  231.      */
  232.     public abstract T getEquinoctialEx();

  234.     /** Get the first component of the equinoctial eccentricity vector.
  235.      * <p>
  236.      * If the orbit was created without derivatives, the value returned is null.
  237.      * </p>
  238.      * @return first component of the equinoctial eccentricity vector
  239.      */
  240.     public abstract T getEquinoctialExDot();

  242.     /** Get the second component of the equinoctial eccentricity vector.
  243.      * @return second component of the equinoctial eccentricity vector
  244.      */
  245.     public abstract T getEquinoctialEy();

  247.     /** Get the second component of the equinoctial eccentricity vector.
  248.      * <p>
  249.      * If the orbit was created without derivatives, the value returned is null.
  250.      * </p>
  251.      * @return second component of the equinoctial eccentricity vector
  252.      */
  253.     public abstract T getEquinoctialEyDot();

  255.     /** Get the first component of the inclination vector.
  256.      * @return first component of the inclination vector
  257.      */
  258.     public abstract T getHx();

  260.     /** Get the first component of the inclination vector derivative.
  261.      * <p>
  262.      * If the orbit was created without derivatives, the value returned is null.
  263.      * </p>
  264.      * @return first component of the inclination vector derivative
  265.      */
  266.     public abstract T getHxDot();

  268.     /** Get the second component of the inclination vector.
  269.      * @return second component of the inclination vector
  270.      */
  271.     public abstract T getHy();

  273.     /** Get the second component of the inclination vector derivative.
  274.      * @return second component of the inclination vector derivative
  275.      */
  276.     public abstract T getHyDot();

  278.     /** Get the eccentric longitude argument.
  279.      * @return E + ω + Ω eccentric longitude argument (rad)
  280.      */
  281.     public abstract T getLE();

  283.     /** Get the eccentric longitude argument derivative.
  284.      * <p>
  285.      * If the orbit was created without derivatives, the value returned is null.
  286.      * </p>
  287.      * @return d(E + ω + Ω)/dt eccentric longitude argument derivative (rad/s)
  288.      */
  289.     public abstract T getLEDot();

  291.     /** Get the true longitude argument.
  292.      * @return v + ω + Ω true longitude argument (rad)
  293.      */
  294.     public abstract T getLv();

  296.     /** Get the true longitude argument derivative.
  297.      * <p>
  298.      * If the orbit was created without derivatives, the value returned is null.
  299.      * </p>
  300.      * @return d(v + ω + Ω)/dt true longitude argument derivative (rad/s)
  301.      */
  302.     public abstract T getLvDot();

  304.     /** Get the mean longitude argument.
  305.      * @return M + ω + Ω mean longitude argument (rad)
  306.      */
  307.     public abstract T getLM();

  309.     /** Get the mean longitude argument derivative.
  310.      * <p>
  311.      * If the orbit was created without derivatives, the value returned is null.
  312.      * </p>
  313.      * @return d(M + ω + Ω)/dt mean longitude argument derivative (rad/s)
  314.      */
  315.     public abstract T getLMDot();

  317.     // Additional orbital elements

  319.     /** Get the eccentricity.
  320.      * @return eccentricity
  321.      */
  322.     public abstract T getE();

  324.     /** Get the eccentricity derivative.
  325.      * <p>
  326.      * If the orbit was created without derivatives, the value returned is null.
  327.      * </p>
  328.      * @return eccentricity derivative
  329.      */
  330.     public abstract T getEDot();

  332.     /** Get the inclination.
  333.      * <p>
  334.      * If the orbit was created without derivatives, the value returned is null.
  335.      * </p>
  336.      * @return inclination (rad)
  337.      */
  338.     public abstract T getI();

  340.     /** Get the inclination derivative.
  341.      * @return inclination derivative (rad/s)
  342.      */
  343.     public abstract T getIDot();

  345.     /** Get the central acceleration constant.
  346.      * @return central acceleration constant
  347.      */

  349.     /** Check if orbit includes derivatives.
  350.      * @return true if orbit includes derivatives
  351.      * @see #getADot()
  352.      * @see #getEquinoctialExDot()
  353.      * @see #getEquinoctialEyDot()
  354.      * @see #getHxDot()
  355.      * @see #getHyDot()
  356.      * @see #getLEDot()
  357.      * @see #getLvDot()
  358.      * @see #getLMDot()
  359.      * @see #getEDot()
  360.      * @see #getIDot()
  361.      * @since 9.0
  362.      */
  363.     public abstract boolean hasDerivatives();

  365.     /** Get the central attraction coefficient used for position and velocity conversions (m³/s²).
  366.      * @return central attraction coefficient used for position and velocity conversions (m³/s²)
  367.      */
  368.     public T getMu() {
  369.         return mu;
  370.     }

  372.     /** Get the Keplerian period.
  373.      * <p>The Keplerian period is computed directly from semi major axis
  374.      * and central acceleration constant.</p>
  375.      * @return Keplerian period in seconds, or positive infinity for hyperbolic orbits
  376.      */
  377.     public T getKeplerianPeriod() {
  378.         final T a = getA();
  379.         return (a.getReal() < 0) ? getA().getField().getZero().add(Double.POSITIVE_INFINITY) : a.multiply(a.getPi().multiply(2.0)).multiply(a.divide(mu).sqrt());
  380.     }

  382.     /** Get the Keplerian mean motion.
  383.      * <p>The Keplerian mean motion is computed directly from semi major axis
  384.      * and central acceleration constant.</p>
  385.      * @return Keplerian mean motion in radians per second
  386.      */
  387.     public T getKeplerianMeanMotion() {
  388.         final T absA = getA().abs();
  389.         return absA.reciprocal().multiply(mu).sqrt().divide(absA);
  390.     }

  392.     /** Get the date of orbital parameters.
  393.      * @return date of the orbital parameters
  394.      */
  395.     public FieldAbsoluteDate<T> getDate() {
  396.         return date;
  397.     }

  399.     /** Get the {@link TimeStampedPVCoordinates} in a specified frame.
  400.      * @param outputFrame frame in which the position/velocity coordinates shall be computed
  401.      * @return FieldPVCoordinates in the specified output frame
  402.           * @see #getPVCoordinates()
  403.      */
  404.     public TimeStampedFieldPVCoordinates<T> getPVCoordinates(final Frame outputFrame) {
  405.         if (pvCoordinates == null) {
  406.             pvCoordinates = initPVCoordinates();
  407.         }

  409.         // If output frame requested is the same as definition frame,
  410.         // PV coordinates are returned directly
  411.         if (outputFrame == frame) {
  412.             return pvCoordinates;
  413.         }

  415.         // Else, PV coordinates are transformed to output frame
  416.         final Transform t = frame.getTransformTo(outputFrame, date.toAbsoluteDate()); //TODO CHECK THIS
  417.         return t.transformPVCoordinates(pvCoordinates);
  418.     }

  420.     /** {@inheritDoc} */
  421.     public TimeStampedFieldPVCoordinates<T> getPVCoordinates(final FieldAbsoluteDate<T> otherDate, final Frame otherFrame) {
  422.         return shiftedBy(otherDate.durationFrom(getDate())).getPVCoordinates(otherFrame);
  423.     }


  426.     /** Get the {@link TimeStampedPVCoordinates} in definition frame.
  427.      * @return FieldPVCoordinates in the definition frame
  428.      * @see #getPVCoordinates(Frame)
  429.      */
  430.     public TimeStampedFieldPVCoordinates<T> getPVCoordinates() {
  431.         if (pvCoordinates == null) {
  432.             pvCoordinates = initPVCoordinates();

  434.         }
  435.         return pvCoordinates;
  436.     }

  438.     /** Compute the position/velocity coordinates from the canonical parameters.
  439.      * @return computed position/velocity coordinates
  440.      */
  441.     protected abstract TimeStampedFieldPVCoordinates<T> initPVCoordinates();

  443.     /** Get a time-shifted orbit.
  444.      * <p>
  445.      * The orbit can be slightly shifted to close dates. This shift is based on
  446.      * a simple Keplerian model. It is <em>not</em> intended as a replacement
  447.      * for proper orbit and attitude propagation but should be sufficient for
  448.      * small time shifts or coarse accuracy.
  449.      * </p>
  450.      * @param dt time shift in seconds
  451.      * @return a new orbit, shifted with respect to the instance (which is immutable)
  452.      */
  453.     public abstract FieldOrbit<T> shiftedBy(T dt);

  455.     /** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
  456.      * <p>
  457.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  458.      * respect to Cartesian coordinate j. This means each row corresponds to one orbital parameter
  459.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  460.      * </p>
  461.      * @param type type of the position angle to use
  462.      * @param jacobian placeholder 6x6 (or larger) matrix to be filled with the Jacobian, if matrix
  463.      * is larger than 6x6, only the 6x6 upper left corner will be modified
  464.      */
  465.     public void getJacobianWrtCartesian(final PositionAngle type, final T[][] jacobian) {

  467.         final T[][] cachedJacobian;
  468.         synchronized (this) {
  469.             switch (type) {
  470.                 case MEAN :
  471.                     if (jacobianMeanWrtCartesian == null) {
  472.                         // first call, we need to compute the Jacobian and cache it
  473.                         jacobianMeanWrtCartesian = computeJacobianMeanWrtCartesian();
  474.                     }
  475.                     cachedJacobian = jacobianMeanWrtCartesian;
  476.                     break;
  477.                 case ECCENTRIC :
  478.                     if (jacobianEccentricWrtCartesian == null) {
  479.                         // first call, we need to compute the Jacobian and cache it
  480.                         jacobianEccentricWrtCartesian = computeJacobianEccentricWrtCartesian();
  481.                     }
  482.                     cachedJacobian = jacobianEccentricWrtCartesian;
  483.                     break;
  484.                 case TRUE :
  485.                     if (jacobianTrueWrtCartesian == null) {
  486.                         // first call, we need to compute the Jacobian and cache it
  487.                         jacobianTrueWrtCartesian = computeJacobianTrueWrtCartesian();
  488.                     }
  489.                     cachedJacobian = jacobianTrueWrtCartesian;
  490.                     break;
  491.                 default :
  492.                     throw new OrekitInternalError(null);
  493.             }
  494.         }

  496.         // fill the user provided array
  497.         for (int i = 0; i < cachedJacobian.length; ++i) {
  498.             System.arraycopy(cachedJacobian[i], 0, jacobian[i], 0, cachedJacobian[i].length);
  499.         }

  501.     }

  503.     /** Compute the Jacobian of the Cartesian parameters with respect to the orbital parameters.
  504.      * <p>
  505.      * Element {@code jacobian[i][j]} is the derivative of Cartesian coordinate i of the orbit with
  506.      * respect to orbital parameter j. This means each row corresponds to one Cartesian coordinate
  507.      * x, y, z, xdot, ydot, zdot whereas columns 0 to 5 correspond to the orbital parameters.
  508.      * </p>
  509.      * @param type type of the position angle to use
  510.      * @param jacobian placeholder 6x6 (or larger) matrix to be filled with the Jacobian, if matrix
  511.      * is larger than 6x6, only the 6x6 upper left corner will be modified
  512.      */
  513.     public void getJacobianWrtParameters(final PositionAngle type, final T[][] jacobian) {

  515.         final T[][] cachedJacobian;
  516.         synchronized (this) {
  517.             switch (type) {
  518.                 case MEAN :
  519.                     if (jacobianWrtParametersMean == null) {
  520.                         // first call, we need to compute the Jacobian and cache it
  521.                         jacobianWrtParametersMean = createInverseJacobian(type);
  522.                     }
  523.                     cachedJacobian = jacobianWrtParametersMean;
  524.                     break;
  525.                 case ECCENTRIC :
  526.                     if (jacobianWrtParametersEccentric == null) {
  527.                         // first call, we need to compute the Jacobian and cache it
  528.                         jacobianWrtParametersEccentric = createInverseJacobian(type);
  529.                     }
  530.                     cachedJacobian = jacobianWrtParametersEccentric;
  531.                     break;
  532.                 case TRUE :
  533.                     if (jacobianWrtParametersTrue == null) {
  534.                         // first call, we need to compute the Jacobian and cache it
  535.                         jacobianWrtParametersTrue = createInverseJacobian(type);
  536.                     }
  537.                     cachedJacobian = jacobianWrtParametersTrue;
  538.                     break;
  539.                 default :
  540.                     throw new OrekitInternalError(null);
  541.             }
  542.         }

  544.         // fill the user-provided array
  545.         for (int i = 0; i < cachedJacobian.length; ++i) {
  546.             System.arraycopy(cachedJacobian[i], 0, jacobian[i], 0, cachedJacobian[i].length);
  547.         }

  549.     }

  551.     /** Create an inverse Jacobian.
  552.      * @param type type of the position angle to use
  553.      * @return inverse Jacobian
  554.      */
  555.     private T[][] createInverseJacobian(final PositionAngle type) {

  557.         // get the direct Jacobian
  558.         final T[][] directJacobian = MathArrays.buildArray(getA().getField(), 6, 6);
  559.         getJacobianWrtCartesian(type, directJacobian);

  561.         // invert the direct Jacobian
  562.         final FieldMatrix<T> matrix = MatrixUtils.createFieldMatrix(directJacobian);
  563.         final FieldDecompositionSolver<T> solver = new FieldLUDecomposition<>(matrix).getSolver();
  564.         return solver.getInverse().getData();

  566.     }

  568.     /** Compute the Jacobian of the orbital parameters with mean angle with respect to the Cartesian parameters.
  569.      * <p>
  570.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  571.      * respect to Cartesian coordinate j. This means each row correspond to one orbital parameter
  572.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  573.      * </p>
  574.      * @return 6x6 Jacobian matrix
  575.      * @see #computeJacobianEccentricWrtCartesian()
  576.      * @see #computeJacobianTrueWrtCartesian()
  577.      */
  578.     protected abstract T[][] computeJacobianMeanWrtCartesian();

  580.     /** Compute the Jacobian of the orbital parameters with eccentric angle with respect to the Cartesian parameters.
  581.      * <p>
  582.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  583.      * respect to Cartesian coordinate j. This means each row correspond to one orbital parameter
  584.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  585.      * </p>
  586.      * @return 6x6 Jacobian matrix
  587.      * @see #computeJacobianMeanWrtCartesian()
  588.      * @see #computeJacobianTrueWrtCartesian()
  589.      */
  590.     protected abstract T[][] computeJacobianEccentricWrtCartesian();

  592.     /** Compute the Jacobian of the orbital parameters with true angle with respect to the Cartesian parameters.
  593.      * <p>
  594.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  595.      * respect to Cartesian coordinate j. This means each row correspond to one orbital parameter
  596.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  597.      * </p>
  598.      * @return 6x6 Jacobian matrix
  599.      * @see #computeJacobianMeanWrtCartesian()
  600.      * @see #computeJacobianEccentricWrtCartesian()
  601.      */
  602.     protected abstract T[][] computeJacobianTrueWrtCartesian();

  604.     /** Add the contribution of the Keplerian motion to parameters derivatives
  605.      * <p>
  606.      * This method is used by integration-based propagators to evaluate the part of Keplerian
  607.      * motion to evolution of the orbital state.
  608.      * </p>
  609.      * @param type type of the position angle in the state
  610.      * @param gm attraction coefficient to use
  611.      * @param pDot array containing orbital state derivatives to update (the Keplerian
  612.      * part must be <em>added</em> to the array components, as the array may already
  613.      * contain some non-zero elements corresponding to non-Keplerian parts)
  614.      */
  615.     public abstract void addKeplerContribution(PositionAngle type, T gm, T[] pDot);

  617.         /** Fill a Jacobian half row with a single vector.
  618.      * @param a coefficient of the vector
  619.      * @param v vector
  620.      * @param row Jacobian matrix row
  621.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  622.      */

  624.     protected void fillHalfRow(final T a, final FieldVector3D<T> v, final T[] row, final int j) {
  625.         row[j]     = a.multiply(v.getX());
  626.         row[j + 1] = a.multiply(v.getY());
  627.         row[j + 2] = a.multiply(v.getZ());
  628.     }

  630.     /** Fill a Jacobian half row with a linear combination of vectors.
  631.      * @param a1 coefficient of the first vector
  632.      * @param v1 first vector
  633.      * @param a2 coefficient of the second vector
  634.      * @param v2 second vector
  635.      * @param row Jacobian matrix row
  636.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  637.      */
  638.     protected void fillHalfRow(final T a1, final FieldVector3D<T> v1, final T a2, final FieldVector3D<T> v2,
  639.                                       final T[] row, final int j) {
  640.         row[j]     = a1.linearCombination(a1, v1.getX(), a2, v2.getX());
  641.         row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY());
  642.         row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ());
  643. //        row[j]     = a1.multiply(v1.getX()).add(a2.multiply(v2.getX()));
  644. //        row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY()));
  645. //        row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ()));
  646.     }

  648.     /** Fill a Jacobian half row with a linear combination of vectors.
  649.      * @param a1 coefficient of the first vector
  650.      * @param v1 first vector
  651.      * @param a2 coefficient of the second vector
  652.      * @param v2 second vector
  653.      * @param a3 coefficient of the third vector
  654.      * @param v3 third vector
  655.      * @param row Jacobian matrix row
  656.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  657.      */
  658.     protected void fillHalfRow(final T a1, final FieldVector3D<T> v1,
  659.                                final T a2, final FieldVector3D<T> v2,
  660.                                final T a3, final FieldVector3D<T> v3,
  661.                                       final T[] row, final int j) {
  662.         row[j]     = a1.linearCombination(a1, v1.getX(), a2, v2.getX(), a3, v3.getX());
  663.         row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY(), a3, v3.getY());
  664.         row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ(), a3, v3.getZ());



  668. //        row[j]     = a1.multiply(v1.getX()).add(a2.multiply(v2.getX())).add(a3.multiply(v3.getX()));
  669. //        row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY())).add(a3.multiply(v3.getY()));
  670. //        row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ())).add(a3.multiply(v3.getZ()));
  671.     }

  673.     /** Fill a Jacobian half row with a linear combination of vectors.
  674.      * @param a1 coefficient of the first vector
  675.      * @param v1 first vector
  676.      * @param a2 coefficient of the second vector
  677.      * @param v2 second vector
  678.      * @param a3 coefficient of the third vector
  679.      * @param v3 third vector
  680.      * @param a4 coefficient of the fourth vector
  681.      * @param v4 fourth vector
  682.      * @param row Jacobian matrix row
  683.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  684.      */
  685.     protected void fillHalfRow(final T a1, final FieldVector3D<T> v1, final T a2, final FieldVector3D<T> v2,
  686.                                       final T a3, final FieldVector3D<T> v3, final T a4, final FieldVector3D<T> v4,
  687.                                       final T[] row, final int j) {
  688.         row[j]     = a1.linearCombination(a1, v1.getX(), a2, v2.getX(), a3, v3.getX(), a4, v4.getX());
  689.         row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY(), a3, v3.getY(), a4, v4.getY());
  690.         row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ(), a3, v3.getZ(), a4, v4.getZ());
  691. //        row[j]     = a1.multiply(v1.getX()).add(a2.multiply(v2.getX())).add(a3.multiply(v3.getX())).add(a4.multiply(v4.getX()));
  692. //        row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY())).add(a3.multiply(v3.getY())).add(a4.multiply(v4.getY()));
  693. //        row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ())).add(a3.multiply(v3.getZ())).add(a4.multiply(v4.getZ()));
  694.     }

  696.     /** Fill a Jacobian half row with a linear combination of vectors.
  697.      * @param a1 coefficient of the first vector
  698.      * @param v1 first vector
  699.      * @param a2 coefficient of the second vector
  700.      * @param v2 second vector
  701.      * @param a3 coefficient of the third vector
  702.      * @param v3 third vector
  703.      * @param a4 coefficient of the fourth vector
  704.      * @param v4 fourth vector
  705.      * @param a5 coefficient of the fifth vector
  706.      * @param v5 fifth vector
  707.      * @param row Jacobian matrix row
  708.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  709.      */
  710.     protected void fillHalfRow(final T a1, final FieldVector3D<T> v1, final T a2, final FieldVector3D<T> v2,
  711.                                       final T a3, final FieldVector3D<T> v3, final T a4, final FieldVector3D<T> v4,
  712.                                       final T a5, final FieldVector3D<T> v5,
  713.                                       final T[] row, final int j) {
  714.         row[j]     = a1.linearCombination(a1, v1.getX(), a2, v2.getX(), a3, v3.getX(), a4, v4.getX()).add(a5.multiply(v5.getX()));
  715.         row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY(), a3, v3.getY(), a4, v4.getY()).add(a5.multiply(v5.getY()));
  716.         row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ(), a3, v3.getZ(), a4, v4.getZ()).add(a5.multiply(v5.getZ()));

  718. //        row[j]     = a1.multiply(v1.getX()).add(a2.multiply(v2.getX())).add(a3.multiply(v3.getX())).add(a4.multiply(v4.getX())).add(a5.multiply(v5.getX()));
  719. //        row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY())).add(a3.multiply(v3.getY())).add(a4.multiply(v4.getY())).add(a5.multiply(v5.getY()));
  720. //        row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ())).add(a3.multiply(v3.getZ())).add(a4.multiply(v4.getZ())).add(a5.multiply(v5.getZ()));
  721.     }

  723.     /** Fill a Jacobian half row with a linear combination of vectors.
  724.      * @param a1 coefficient of the first vector
  725.      * @param v1 first vector
  726.      * @param a2 coefficient of the second vector
  727.      * @param v2 second vector
  728.      * @param a3 coefficient of the third vector
  729.      * @param v3 third vector
  730.      * @param a4 coefficient of the fourth vector
  731.      * @param v4 fourth vector
  732.      * @param a5 coefficient of the fifth vector
  733.      * @param v5 fifth vector
  734.      * @param a6 coefficient of the sixth vector
  735.      * @param v6 sixth vector
  736.      * @param row Jacobian matrix row
  737.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  738.      */
  739.     protected void fillHalfRow(final T a1, final FieldVector3D<T> v1, final T a2, final FieldVector3D<T> v2,
  740.                                       final T a3, final FieldVector3D<T> v3, final T a4, final FieldVector3D<T> v4,
  741.                                       final T a5, final FieldVector3D<T> v5, final T a6, final FieldVector3D<T> v6,
  742.                                       final T[] row, final int j) {
  743.         row[j]     = a1.linearCombination(a1, v1.getX(), a2, v2.getX(), a3, v3.getX(), a4, v4.getX()).add(a1.linearCombination(a5, v5.getX(), a6, v6.getX()));
  744.         row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY(), a3, v3.getY(), a4, v4.getY()).add(a1.linearCombination(a5, v5.getY(), a6, v6.getY()));
  745.         row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ(), a3, v3.getZ(), a4, v4.getZ()).add(a1.linearCombination(a5, v5.getZ(), a6, v6.getZ()));


  748. //        row[j]     = a1.multiply(v1.getX()).add(a2.multiply(v2.getX())).add(a3.multiply(v3.getX())).add(a4.multiply(v4.getX())).add(a5.multiply(v5.getX())).add(a6.multiply(v6.getX()));
  749. //        row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY())).add(a3.multiply(v3.getY())).add(a4.multiply(v4.getY())).add(a5.multiply(v5.getY())).add(a6.multiply(v6.getY()));
  750. //        row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ())).add(a3.multiply(v3.getZ())).add(a4.multiply(v4.getZ())).add(a5.multiply(v5.getZ())).add(a6.multiply(v6.getZ()));
  751.     }


  754. }
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