Orbit.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;

  19. import java.io.Serializable;

  21. import org.hipparchus.geometry.euclidean.threed.Vector3D;
  22. import org.hipparchus.linear.DecompositionSolver;
  23. import org.hipparchus.linear.MatrixUtils;
  24. import org.hipparchus.linear.QRDecomposition;
  25. import org.hipparchus.linear.RealMatrix;
  26. import org.hipparchus.util.FastMath;
  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.AbsoluteDate;
  34. import org.orekit.time.TimeInterpolable;
  35. import org.orekit.time.TimeShiftable;
  36. import org.orekit.time.TimeStamped;
  37. import org.orekit.utils.PVCoordinates;
  38. import org.orekit.utils.PVCoordinatesProvider;
  39. import org.orekit.utils.TimeStampedPVCoordinates;

  41. /**
  42.  * This class handles orbital parameters.

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

  68.     /** Serializable UID. */
  69.     private static final long serialVersionUID = 438733454597999578L;

  71.     /** Frame in which are defined the orbital parameters. */
  72.     private final Frame frame;

  74.     /** Date of the orbital parameters. */
  75.     private final AbsoluteDate date;

  77.     /** Value of mu used to compute position and velocity (m³/s²). */
  78.     private final double mu;

  80.     /** Computed PVCoordinates. */
  81.     private transient TimeStampedPVCoordinates pvCoordinates;

  83.     /** Jacobian of the orbital parameters with mean angle with respect to the Cartesian coordinates. */
  84.     private transient double[][] jacobianMeanWrtCartesian;

  86.     /** Jacobian of the Cartesian coordinates with respect to the orbital parameters with mean angle. */
  87.     private transient double[][] jacobianWrtParametersMean;

  89.     /** Jacobian of the orbital parameters with eccentric angle with respect to the Cartesian coordinates. */
  90.     private transient double[][] jacobianEccentricWrtCartesian;

  92.     /** Jacobian of the Cartesian coordinates with respect to the orbital parameters with eccentric angle. */
  93.     private transient double[][] jacobianWrtParametersEccentric;

  95.     /** Jacobian of the orbital parameters with true angle with respect to the Cartesian coordinates. */
  96.     private transient double[][] jacobianTrueWrtCartesian;

  98.     /** Jacobian of the Cartesian coordinates with respect to the orbital parameters with true angle. */
  99.     private transient double[][] jacobianWrtParametersTrue;

  101.     /** Default constructor.
  102.      * Build a new instance with arbitrary default elements.
  103.      * @param frame the frame in which the parameters are defined
  104.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  105.      * @param date date of the orbital parameters
  106.      * @param mu central attraction coefficient (m^3/s^2)
  107.      * @exception IllegalArgumentException if frame is not a {@link
  108.      * Frame#isPseudoInertial pseudo-inertial frame}
  109.      */
  110.     protected Orbit(final Frame frame, final AbsoluteDate date, final double mu)
  111.         throws IllegalArgumentException {
  112.         ensurePseudoInertialFrame(frame);
  113.         this.date                      = date;
  114.         this.mu                        = mu;
  115.         this.pvCoordinates             = null;
  116.         this.frame                     = frame;
  117.         jacobianMeanWrtCartesian       = null;
  118.         jacobianWrtParametersMean      = null;
  119.         jacobianEccentricWrtCartesian  = null;
  120.         jacobianWrtParametersEccentric = null;
  121.         jacobianTrueWrtCartesian       = null;
  122.         jacobianWrtParametersTrue      = null;
  123.     }

  125.     /** Set the orbit from Cartesian parameters.
  126.      *
  127.      * <p> The acceleration provided in {@code pvCoordinates} is accessible using
  128.      * {@link #getPVCoordinates()} and {@link #getPVCoordinates(Frame)}. All other methods
  129.      * use {@code mu} and the position to compute the acceleration, including
  130.      * {@link #shiftedBy(double)} and {@link #getPVCoordinates(AbsoluteDate, Frame)}.
  131.      *
  132.      * @param pvCoordinates the position and velocity in the inertial frame
  133.      * @param frame the frame in which the {@link TimeStampedPVCoordinates} are defined
  134.      * (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
  135.      * @param mu central attraction coefficient (m^3/s^2)
  136.      * @exception IllegalArgumentException if frame is not a {@link
  137.      * Frame#isPseudoInertial pseudo-inertial frame}
  138.      */
  139.     protected Orbit(final TimeStampedPVCoordinates pvCoordinates, final Frame frame, final double mu)
  140.         throws IllegalArgumentException {
  141.         ensurePseudoInertialFrame(frame);
  142.         this.date = pvCoordinates.getDate();
  143.         this.mu = mu;
  144.         if (pvCoordinates.getAcceleration().getNormSq() == 0) {
  145.             // the acceleration was not provided,
  146.             // compute it from Newtonian attraction
  147.             final double r2 = pvCoordinates.getPosition().getNormSq();
  148.             final double r3 = r2 * FastMath.sqrt(r2);
  149.             this.pvCoordinates = new TimeStampedPVCoordinates(pvCoordinates.getDate(),
  150.                                                               pvCoordinates.getPosition(),
  151.                                                               pvCoordinates.getVelocity(),
  152.                                                               new Vector3D(-mu / r3, pvCoordinates.getPosition()));
  153.         } else {
  154.             this.pvCoordinates = pvCoordinates;
  155.         }
  156.         this.frame = frame;
  157.     }

  159.     /** Check if Cartesian coordinates include non-Keplerian acceleration.
  160.      * @param pva Cartesian coordinates
  161.      * @param mu central attraction coefficient
  162.      * @return true if Cartesian coordinates include non-Keplerian acceleration
  163.      */
  164.     protected static boolean hasNonKeplerianAcceleration(final PVCoordinates pva, final double mu) {

  166.         final Vector3D p = pva.getPosition();
  167.         final double r2 = p.getNormSq();
  168.         final double r  = FastMath.sqrt(r2);
  169.         final Vector3D keplerianAcceleration = new Vector3D(-mu / (r * r2), p);

  171.         // Check if acceleration is null or relatively close to 0 compared to the keplerain acceleration
  172.         final Vector3D a = pva.getAcceleration();
  173.         if (a == null || a.getNorm() < 1e-9 * keplerianAcceleration.getNorm()) {
  174.             return false;
  175.         }

  177.         final Vector3D nonKeplerianAcceleration = a.subtract(keplerianAcceleration);

  179.         if ( nonKeplerianAcceleration.getNorm() > 1e-9 * keplerianAcceleration.getNorm()) {
  180.             // we have a relevant acceleration, we can compute derivatives
  181.             return true;
  182.         } else {
  183.             // the provided acceleration is either too small to be reliable (probably even 0), or NaN
  184.             return false;
  185.         }
  186.     }

  188.     /** Get the orbit type.
  189.      * @return orbit type
  190.      */
  191.     public abstract OrbitType getType();

  193.     /** Ensure the defining frame is a pseudo-inertial frame.
  194.      * @param frame frame to check
  195.      * @exception IllegalArgumentException if frame is not a {@link
  196.      * Frame#isPseudoInertial pseudo-inertial frame}
  197.      */
  198.     private static void ensurePseudoInertialFrame(final Frame frame)
  199.         throws IllegalArgumentException {
  200.         if (!frame.isPseudoInertial()) {
  201.             throw new OrekitIllegalArgumentException(OrekitMessages.NON_PSEUDO_INERTIAL_FRAME,
  202.                                                      frame.getName());
  203.         }
  204.     }

  206.     /** Get the frame in which the orbital parameters are defined.
  207.      * @return frame in which the orbital parameters are defined
  208.      */
  209.     public Frame getFrame() {
  210.         return frame;
  211.     }

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

  219.     /** Get the semi-major axis derivative.
  220.      * <p>Note that the semi-major axis is considered negative for hyperbolic orbits.</p>
  221.      * <p>
  222.      * If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
  223.      * </p>
  224.      * @return semi-major axis  derivative (m/s)
  225.      * @see #hasDerivatives()
  226.      * @since 9.0
  227.      */
  228.     public abstract double getADot();

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

  235.     /** Get the first component of the equinoctial eccentricity vector.
  236.      * <p>
  237.      * If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
  238.      * </p>
  239.      * @return first component of the equinoctial eccentricity vector
  240.      * @see #hasDerivatives()
  241.      * @since 9.0
  242.      */
  243.     public abstract double getEquinoctialExDot();

  245.     /** Get the second component of the equinoctial eccentricity vector derivative.
  246.      * @return second component of the equinoctial eccentricity vector derivative
  247.      */
  248.     public abstract double getEquinoctialEy();

  250.     /** Get the second component of the equinoctial eccentricity vector.
  251.      * <p>
  252.      * If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
  253.      * </p>
  254.      * @return second component of the equinoctial eccentricity vector
  255.      * @see #hasDerivatives()
  256.      * @since 9.0
  257.      */
  258.     public abstract double getEquinoctialEyDot();

  260.     /** Get the first component of the inclination vector.
  261.      * @return first component of the inclination vector
  262.      */
  263.     public abstract double getHx();

  265.     /** Get the first component of the inclination vector derivative.
  266.      * <p>
  267.      * If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
  268.      * </p>
  269.      * @return first component of the inclination vector derivative
  270.      * @see #hasDerivatives()
  271.      * @since 9.0
  272.      */
  273.     public abstract double getHxDot();

  275.     /** Get the second component of the inclination vector.
  276.      * @return second component of the inclination vector
  277.      */
  278.     public abstract double getHy();

  280.     /** Get the second component of the inclination vector derivative.
  281.      * <p>
  282.      * If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
  283.      * </p>
  284.      * @return second component of the inclination vector derivative
  285.      * @see #hasDerivatives()
  286.      * @since 9.0
  287.      */
  288.     public abstract double getHyDot();

  290.     /** Get the eccentric longitude argument.
  291.      * @return E + ω + Ω eccentric longitude argument (rad)
  292.      */
  293.     public abstract double getLE();

  295.     /** Get the eccentric longitude argument derivative.
  296.      * <p>
  297.      * If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
  298.      * </p>
  299.      * @return d(E + ω + Ω)/dt eccentric longitude argument derivative (rad/s)
  300.      * @see #hasDerivatives()
  301.      * @since 9.0
  302.      */
  303.     public abstract double getLEDot();

  305.     /** Get the true longitude argument.
  306.      * @return v + ω + Ω true longitude argument (rad)
  307.      */
  308.     public abstract double getLv();

  310.     /** Get the true longitude argument derivative.
  311.      * <p>
  312.      * If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
  313.      * </p>
  314.      * @return d(v + ω + Ω)/dt true longitude argument derivative (rad/s)
  315.      * @see #hasDerivatives()
  316.      * @since 9.0
  317.      */
  318.     public abstract double getLvDot();

  320.     /** Get the mean longitude argument.
  321.      * @return M + ω + Ω mean longitude argument (rad)
  322.      */
  323.     public abstract double getLM();

  325.     /** Get the mean longitude argument derivative.
  326.      * <p>
  327.      * If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
  328.      * </p>
  329.      * @return d(M + ω + Ω)/dt mean longitude argument derivative (rad/s)
  330.      * @see #hasDerivatives()
  331.      * @since 9.0
  332.      */
  333.     public abstract double getLMDot();

  335.     // Additional orbital elements

  337.     /** Get the eccentricity.
  338.      * @return eccentricity
  339.      */
  340.     public abstract double getE();

  342.     /** Get the eccentricity derivative.
  343.      * <p>
  344.      * If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
  345.      * </p>
  346.      * @return eccentricity derivative
  347.      * @see #hasDerivatives()
  348.      * @since 9.0
  349.      */
  350.     public abstract double getEDot();

  352.     /** Get the inclination.
  353.      * @return inclination (rad)
  354.      */
  355.     public abstract double getI();

  357.     /** Get the inclination derivative.
  358.      * <p>
  359.      * If the orbit was created without derivatives, the value returned is {@link Double#NaN}.
  360.      * </p>
  361.      * @return inclination derivative (rad/s)
  362.      * @see #hasDerivatives()
  363.      * @since 9.0
  364.      */
  365.     public abstract double getIDot();

  367.     /** Check if orbit includes derivatives.
  368.      * @return true if orbit includes derivatives
  369.      * @see #getADot()
  370.      * @see #getEquinoctialExDot()
  371.      * @see #getEquinoctialEyDot()
  372.      * @see #getHxDot()
  373.      * @see #getHyDot()
  374.      * @see #getLEDot()
  375.      * @see #getLvDot()
  376.      * @see #getLMDot()
  377.      * @see #getEDot()
  378.      * @see #getIDot()
  379.      * @since 9.0
  380.      */
  381.     public boolean hasDerivatives() {
  382.         return !Double.isNaN(getADot());
  383.     }

  385.     /** Get the central acceleration constant.
  386.      * @return central acceleration constant
  387.      */
  388.     public double getMu() {
  389.         return mu;
  390.     }

  392.     /** Get the Keplerian period.
  393.      * <p>The Keplerian period is computed directly from semi major axis
  394.      * and central acceleration constant.</p>
  395.      * @return Keplerian period in seconds, or positive infinity for hyperbolic orbits
  396.      */
  397.     public double getKeplerianPeriod() {
  398.         final double a = getA();
  399.         return (a < 0) ? Double.POSITIVE_INFINITY : 2.0 * FastMath.PI * a * FastMath.sqrt(a / mu);
  400.     }

  402.     /** Get the Keplerian mean motion.
  403.      * <p>The Keplerian mean motion is computed directly from semi major axis
  404.      * and central acceleration constant.</p>
  405.      * @return Keplerian mean motion in radians per second
  406.      */
  407.     public double getKeplerianMeanMotion() {
  408.         final double absA = FastMath.abs(getA());
  409.         return FastMath.sqrt(mu / absA) / absA;
  410.     }

  412.     /** Get the date of orbital parameters.
  413.      * @return date of the orbital parameters
  414.      */
  415.     public AbsoluteDate getDate() {
  416.         return date;
  417.     }

  419.     /** Get the {@link TimeStampedPVCoordinates} in a specified frame.
  420.      * @param outputFrame frame in which the position/velocity coordinates shall be computed
  421.      * @return pvCoordinates in the specified output frame
  422.           * @see #getPVCoordinates()
  423.      */
  424.     public TimeStampedPVCoordinates getPVCoordinates(final Frame outputFrame) {
  425.         if (pvCoordinates == null) {
  426.             pvCoordinates = initPVCoordinates();
  427.         }

  429.         // If output frame requested is the same as definition frame,
  430.         // PV coordinates are returned directly
  431.         if (outputFrame == frame) {
  432.             return pvCoordinates;
  433.         }

  435.         // Else, PV coordinates are transformed to output frame
  436.         final Transform t = frame.getTransformTo(outputFrame, date);
  437.         return t.transformPVCoordinates(pvCoordinates);
  438.     }

  440.     /** {@inheritDoc} */
  441.     public TimeStampedPVCoordinates getPVCoordinates(final AbsoluteDate otherDate, final Frame otherFrame) {
  442.         return shiftedBy(otherDate.durationFrom(getDate())).getPVCoordinates(otherFrame);
  443.     }


  446.     /** Get the {@link TimeStampedPVCoordinates} in definition frame.
  447.      * @return pvCoordinates in the definition frame
  448.      * @see #getPVCoordinates(Frame)
  449.      */
  450.     public TimeStampedPVCoordinates getPVCoordinates() {
  451.         if (pvCoordinates == null) {
  452.             pvCoordinates = initPVCoordinates();
  453.         }
  454.         return pvCoordinates;
  455.     }

  457.     /** Compute the position/velocity coordinates from the canonical parameters.
  458.      * @return computed position/velocity coordinates
  459.      */
  460.     protected abstract TimeStampedPVCoordinates initPVCoordinates();

  462.     /** Get a time-shifted orbit.
  463.      * <p>
  464.      * The orbit can be slightly shifted to close dates. The shifting model is a
  465.      * Keplerian one if no derivatives are available in the orbit, or Keplerian
  466.      * plus quadratic effect of the non-Keplerian acceleration if derivatives are
  467.      * available. Shifting is <em>not</em> intended as a replacement for proper
  468.      * orbit propagation but should be sufficient for small time shifts or coarse
  469.      * accuracy.
  470.      * </p>
  471.      * @param dt time shift in seconds
  472.      * @return a new orbit, shifted with respect to the instance (which is immutable)
  473.      */
  474.     public abstract Orbit shiftedBy(double dt);

  476.     /** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
  477.      * <p>
  478.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  479.      * respect to Cartesian coordinate j. This means each row corresponds to one orbital parameter
  480.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  481.      * </p>
  482.      * @param type type of the position angle to use
  483.      * @param jacobian placeholder 6x6 (or larger) matrix to be filled with the Jacobian, if matrix
  484.      * is larger than 6x6, only the 6x6 upper left corner will be modified
  485.      */
  486.     public void getJacobianWrtCartesian(final PositionAngle type, final double[][] jacobian) {

  488.         final double[][] cachedJacobian;
  489.         synchronized (this) {
  490.             switch (type) {
  491.                 case MEAN :
  492.                     if (jacobianMeanWrtCartesian == null) {
  493.                         // first call, we need to compute the Jacobian and cache it
  494.                         jacobianMeanWrtCartesian = computeJacobianMeanWrtCartesian();
  495.                     }
  496.                     cachedJacobian = jacobianMeanWrtCartesian;
  497.                     break;
  498.                 case ECCENTRIC :
  499.                     if (jacobianEccentricWrtCartesian == null) {
  500.                         // first call, we need to compute the Jacobian and cache it
  501.                         jacobianEccentricWrtCartesian = computeJacobianEccentricWrtCartesian();
  502.                     }
  503.                     cachedJacobian = jacobianEccentricWrtCartesian;
  504.                     break;
  505.                 case TRUE :
  506.                     if (jacobianTrueWrtCartesian == null) {
  507.                         // first call, we need to compute the Jacobian and cache it
  508.                         jacobianTrueWrtCartesian = computeJacobianTrueWrtCartesian();
  509.                     }
  510.                     cachedJacobian = jacobianTrueWrtCartesian;
  511.                     break;
  512.                 default :
  513.                     throw new OrekitInternalError(null);
  514.             }
  515.         }

  517.         // fill the user provided array
  518.         for (int i = 0; i < cachedJacobian.length; ++i) {
  519.             System.arraycopy(cachedJacobian[i], 0, jacobian[i], 0, cachedJacobian[i].length);
  520.         }

  522.     }

  524.     /** Compute the Jacobian of the Cartesian parameters with respect to the orbital parameters.
  525.      * <p>
  526.      * Element {@code jacobian[i][j]} is the derivative of Cartesian coordinate i of the orbit with
  527.      * respect to orbital parameter j. This means each row corresponds to one Cartesian coordinate
  528.      * x, y, z, xdot, ydot, zdot whereas columns 0 to 5 correspond to the orbital parameters.
  529.      * </p>
  530.      * @param type type of the position angle to use
  531.      * @param jacobian placeholder 6x6 (or larger) matrix to be filled with the Jacobian, if matrix
  532.      * is larger than 6x6, only the 6x6 upper left corner will be modified
  533.      */
  534.     public void getJacobianWrtParameters(final PositionAngle type, final double[][] jacobian) {

  536.         final double[][] cachedJacobian;
  537.         synchronized (this) {
  538.             switch (type) {
  539.                 case MEAN :
  540.                     if (jacobianWrtParametersMean == null) {
  541.                         // first call, we need to compute the Jacobian and cache it
  542.                         jacobianWrtParametersMean = createInverseJacobian(type);
  543.                     }
  544.                     cachedJacobian = jacobianWrtParametersMean;
  545.                     break;
  546.                 case ECCENTRIC :
  547.                     if (jacobianWrtParametersEccentric == null) {
  548.                         // first call, we need to compute the Jacobian and cache it
  549.                         jacobianWrtParametersEccentric = createInverseJacobian(type);
  550.                     }
  551.                     cachedJacobian = jacobianWrtParametersEccentric;
  552.                     break;
  553.                 case TRUE :
  554.                     if (jacobianWrtParametersTrue == null) {
  555.                         // first call, we need to compute the Jacobian and cache it
  556.                         jacobianWrtParametersTrue = createInverseJacobian(type);
  557.                     }
  558.                     cachedJacobian = jacobianWrtParametersTrue;
  559.                     break;
  560.                 default :
  561.                     throw new OrekitInternalError(null);
  562.             }
  563.         }

  565.         // fill the user-provided array
  566.         for (int i = 0; i < cachedJacobian.length; ++i) {
  567.             System.arraycopy(cachedJacobian[i], 0, jacobian[i], 0, cachedJacobian[i].length);
  568.         }

  570.     }

  572.     /** Create an inverse Jacobian.
  573.      * @param type type of the position angle to use
  574.      * @return inverse Jacobian
  575.      */
  576.     private double[][] createInverseJacobian(final PositionAngle type) {

  578.         // get the direct Jacobian
  579.         final double[][] directJacobian = new double[6][6];
  580.         getJacobianWrtCartesian(type, directJacobian);

  582.         // invert the direct Jacobian
  583.         final RealMatrix matrix = MatrixUtils.createRealMatrix(directJacobian);
  584.         final DecompositionSolver solver = new QRDecomposition(matrix).getSolver();
  585.         return solver.getInverse().getData();

  587.     }

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

  601.     /** Compute the Jacobian of the orbital parameters with eccentric angle with respect to the Cartesian parameters.
  602.      * <p>
  603.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  604.      * respect to Cartesian coordinate j. This means each row correspond to one orbital parameter
  605.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  606.      * </p>
  607.      * @return 6x6 Jacobian matrix
  608.      * @see #computeJacobianMeanWrtCartesian()
  609.      * @see #computeJacobianTrueWrtCartesian()
  610.      */
  611.     protected abstract double[][] computeJacobianEccentricWrtCartesian();

  613.     /** Compute the Jacobian of the orbital parameters with true angle with respect to the Cartesian parameters.
  614.      * <p>
  615.      * Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
  616.      * respect to Cartesian coordinate j. This means each row correspond to one orbital parameter
  617.      * whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
  618.      * </p>
  619.      * @return 6x6 Jacobian matrix
  620.      * @see #computeJacobianMeanWrtCartesian()
  621.      * @see #computeJacobianEccentricWrtCartesian()
  622.      */
  623.     protected abstract double[][] computeJacobianTrueWrtCartesian();

  625.     /** Add the contribution of the Keplerian motion to parameters derivatives
  626.      * <p>
  627.      * This method is used by integration-based propagators to evaluate the part of Keplerian
  628.      * motion to evolution of the orbital state.
  629.      * </p>
  630.      * @param type type of the position angle in the state
  631.      * @param gm attraction coefficient to use
  632.      * @param pDot array containing orbital state derivatives to update (the Keplerian
  633.      * part must be <em>added</em> to the array components, as the array may already
  634.      * contain some non-zero elements corresponding to non-Keplerian parts)
  635.      */
  636.     public abstract void addKeplerContribution(PositionAngle type, double gm, double[] pDot);

  638.         /** Fill a Jacobian half row with a single vector.
  639.      * @param a coefficient of the vector
  640.      * @param v vector
  641.      * @param row Jacobian matrix row
  642.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  643.      */
  644.     protected static void fillHalfRow(final double a, final Vector3D v, final double[] row, final int j) {
  645.         row[j]     = a * v.getX();
  646.         row[j + 1] = a * v.getY();
  647.         row[j + 2] = a * v.getZ();
  648.     }

  650.     /** Fill a Jacobian half row with a linear combination of vectors.
  651.      * @param a1 coefficient of the first vector
  652.      * @param v1 first vector
  653.      * @param a2 coefficient of the second vector
  654.      * @param v2 second 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 static void fillHalfRow(final double a1, final Vector3D v1, final double a2, final Vector3D v2,
  659.                                       final double[] row, final int j) {
  660.         row[j]     = MathArrays.linearCombination(a1, v1.getX(), a2, v2.getX());
  661.         row[j + 1] = MathArrays.linearCombination(a1, v1.getY(), a2, v2.getY());
  662.         row[j + 2] = MathArrays.linearCombination(a1, v1.getZ(), a2, v2.getZ());
  663.     }

  665.     /** Fill a Jacobian half row with a linear combination of vectors.
  666.      * @param a1 coefficient of the first vector
  667.      * @param v1 first vector
  668.      * @param a2 coefficient of the second vector
  669.      * @param v2 second vector
  670.      * @param a3 coefficient of the third vector
  671.      * @param v3 third vector
  672.      * @param row Jacobian matrix row
  673.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  674.      */
  675.     protected static void fillHalfRow(final double a1, final Vector3D v1, final double a2, final Vector3D v2,
  676.                                       final double a3, final Vector3D v3,
  677.                                       final double[] row, final int j) {
  678.         row[j]     = MathArrays.linearCombination(a1, v1.getX(), a2, v2.getX(), a3, v3.getX());
  679.         row[j + 1] = MathArrays.linearCombination(a1, v1.getY(), a2, v2.getY(), a3, v3.getY());
  680.         row[j + 2] = MathArrays.linearCombination(a1, v1.getZ(), a2, v2.getZ(), a3, v3.getZ());
  681.     }

  683.     /** Fill a Jacobian half row with a linear combination of vectors.
  684.      * @param a1 coefficient of the first vector
  685.      * @param v1 first vector
  686.      * @param a2 coefficient of the second vector
  687.      * @param v2 second vector
  688.      * @param a3 coefficient of the third vector
  689.      * @param v3 third vector
  690.      * @param a4 coefficient of the fourth vector
  691.      * @param v4 fourth vector
  692.      * @param row Jacobian matrix row
  693.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  694.      */
  695.     protected static void fillHalfRow(final double a1, final Vector3D v1, final double a2, final Vector3D v2,
  696.                                       final double a3, final Vector3D v3, final double a4, final Vector3D v4,
  697.                                       final double[] row, final int j) {
  698.         row[j]     = MathArrays.linearCombination(a1, v1.getX(), a2, v2.getX(), a3, v3.getX(), a4, v4.getX());
  699.         row[j + 1] = MathArrays.linearCombination(a1, v1.getY(), a2, v2.getY(), a3, v3.getY(), a4, v4.getY());
  700.         row[j + 2] = MathArrays.linearCombination(a1, v1.getZ(), a2, v2.getZ(), a3, v3.getZ(), a4, v4.getZ());
  701.     }

  703.     /** Fill a Jacobian half row with a linear combination of vectors.
  704.      * @param a1 coefficient of the first vector
  705.      * @param v1 first vector
  706.      * @param a2 coefficient of the second vector
  707.      * @param v2 second vector
  708.      * @param a3 coefficient of the third vector
  709.      * @param v3 third vector
  710.      * @param a4 coefficient of the fourth vector
  711.      * @param v4 fourth vector
  712.      * @param a5 coefficient of the fifth vector
  713.      * @param v5 fifth vector
  714.      * @param row Jacobian matrix row
  715.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  716.      */
  717.     protected static void fillHalfRow(final double a1, final Vector3D v1, final double a2, final Vector3D v2,
  718.                                       final double a3, final Vector3D v3, final double a4, final Vector3D v4,
  719.                                       final double a5, final Vector3D v5,
  720.                                       final double[] row, final int j) {
  721.         final double[] a = new double[] {
  722.             a1, a2, a3, a4, a5
  723.         };
  724.         row[j]     = MathArrays.linearCombination(a, new double[] {
  725.             v1.getX(), v2.getX(), v3.getX(), v4.getX(), v5.getX()
  726.         });
  727.         row[j + 1] = MathArrays.linearCombination(a, new double[] {
  728.             v1.getY(), v2.getY(), v3.getY(), v4.getY(), v5.getY()
  729.         });
  730.         row[j + 2] = MathArrays.linearCombination(a, new double[] {
  731.             v1.getZ(), v2.getZ(), v3.getZ(), v4.getZ(), v5.getZ()
  732.         });
  733.     }

  735.     /** Fill a Jacobian half row with a linear combination of vectors.
  736.      * @param a1 coefficient of the first vector
  737.      * @param v1 first vector
  738.      * @param a2 coefficient of the second vector
  739.      * @param v2 second vector
  740.      * @param a3 coefficient of the third vector
  741.      * @param v3 third vector
  742.      * @param a4 coefficient of the fourth vector
  743.      * @param v4 fourth vector
  744.      * @param a5 coefficient of the fifth vector
  745.      * @param v5 fifth vector
  746.      * @param a6 coefficient of the sixth vector
  747.      * @param v6 sixth vector
  748.      * @param row Jacobian matrix row
  749.      * @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
  750.      */
  751.     protected static void fillHalfRow(final double a1, final Vector3D v1, final double a2, final Vector3D v2,
  752.                                       final double a3, final Vector3D v3, final double a4, final Vector3D v4,
  753.                                       final double a5, final Vector3D v5, final double a6, final Vector3D v6,
  754.                                       final double[] row, final int j) {
  755.         final double[] a = new double[] {
  756.             a1, a2, a3, a4, a5, a6
  757.         };
  758.         row[j]     = MathArrays.linearCombination(a, new double[] {
  759.             v1.getX(), v2.getX(), v3.getX(), v4.getX(), v5.getX(), v6.getX()
  760.         });
  761.         row[j + 1] = MathArrays.linearCombination(a, new double[] {
  762.             v1.getY(), v2.getY(), v3.getY(), v4.getY(), v5.getY(), v6.getY()
  763.         });
  764.         row[j + 2] = MathArrays.linearCombination(a, new double[] {
  765.             v1.getZ(), v2.getZ(), v3.getZ(), v4.getZ(), v5.getZ(), v6.getZ()
  766.         });
  767.     }

  769. }
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