PVCoordinates.java

  1. /* Copyright 2002-2025 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.utils;

  19. import org.hipparchus.analysis.differentiation.DSFactory;
  20. import org.hipparchus.analysis.differentiation.Derivative;
  21. import org.hipparchus.analysis.differentiation.DerivativeStructure;
  22. import org.hipparchus.analysis.differentiation.UnivariateDerivative1;
  23. import org.hipparchus.analysis.differentiation.UnivariateDerivative2;
  24. import org.hipparchus.exception.MathIllegalArgumentException;
  25. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  26. import org.hipparchus.geometry.euclidean.threed.Vector3D;
  27. import org.hipparchus.util.Blendable;
  28. import org.hipparchus.util.FastMath;
  29. import org.orekit.errors.OrekitException;
  30. import org.orekit.errors.OrekitMessages;
  31. import org.orekit.time.TimeShiftable;

  33. /** Simple container for Position/Velocity/Acceleration triplets.
  34.  * <p>
  35.  * The state can be slightly shifted to close dates. This shift is based on
  36.  * a simple quadratic model. It is <em>not</em> intended as a replacement for
  37.  * proper orbit propagation (it is not even Keplerian!) but should be sufficient
  38.  * for either small time shifts or coarse accuracy.
  39.  * </p>
  40.  * <p>
  41.  * This class is the angular counterpart to {@link AngularCoordinates}.
  42.  * </p>
  43.  * <p>Instances of this class are guaranteed to be immutable.</p>
  44.  * @author Fabien Maussion
  45.  * @author Luc Maisonobe
  46.  */
  47. public class PVCoordinates implements TimeShiftable<PVCoordinates>, Blendable<PVCoordinates> {

  49.     /** Fixed position/velocity at origin (both p, v and a are zero vectors). */
  50.     public static final PVCoordinates ZERO = new PVCoordinates(Vector3D.ZERO, Vector3D.ZERO, Vector3D.ZERO);

  52.     /** The position. */
  53.     private final Vector3D position;

  55.     /** The velocity. */
  56.     private final Vector3D velocity;

  58.     /** The acceleration. */
  59.     private final Vector3D acceleration;

  61.     /** Simple constructor.
  62.      * <p> Set the Coordinates to default : (0 0 0), (0 0 0), (0 0 0).</p>
  63.      */
  64.     public PVCoordinates() {
  65.         position     = Vector3D.ZERO;
  66.         velocity     = Vector3D.ZERO;
  67.         acceleration = Vector3D.ZERO;
  68.     }

  70.     /** Builds a PVCoordinates triplet with zero acceleration.
  71.      * <p>Acceleration is set to zero</p>
  72.      * @param position the position vector (m)
  73.      * @param velocity the velocity vector (m/s)
  74.      */
  75.     public PVCoordinates(final Vector3D position, final Vector3D velocity) {
  76.         this.position     = position;
  77.         this.velocity     = velocity;
  78.         this.acceleration = Vector3D.ZERO;
  79.     }

  81.     /** Builds a PVCoordinates triplet.
  82.      * @param position the position vector (m)
  83.      * @param velocity the velocity vector (m/s)
  84.      * @param acceleration the acceleration vector (m/s²)
  85.      */
  86.     public PVCoordinates(final Vector3D position, final Vector3D velocity, final Vector3D acceleration) {
  87.         this.position     = position;
  88.         this.velocity     = velocity;
  89.         this.acceleration = acceleration;
  90.     }

  92.     /** Multiplicative constructor.
  93.      * <p>Build a PVCoordinates from another one and a scale factor.</p>
  94.      * <p>The PVCoordinates built will be a * pv</p>
  95.      * @param a scale factor
  96.      * @param pv base (unscaled) PVCoordinates
  97.      */
  98.     public PVCoordinates(final double a, final PVCoordinates pv) {
  99.         position     = new Vector3D(a, pv.position);
  100.         velocity     = new Vector3D(a, pv.velocity);
  101.         acceleration = new Vector3D(a, pv.acceleration);
  102.     }

  104.     /** Subtractive constructor.
  105.      * <p>Build a relative PVCoordinates from a start and an end position.</p>
  106.      * <p>The PVCoordinates built will be end - start.</p>
  107.      * @param start Starting PVCoordinates
  108.      * @param end ending PVCoordinates
  109.      */
  110.     public PVCoordinates(final PVCoordinates start, final PVCoordinates end) {
  111.         this.position     = end.position.subtract(start.position);
  112.         this.velocity     = end.velocity.subtract(start.velocity);
  113.         this.acceleration = end.acceleration.subtract(start.acceleration);
  114.     }

  116.     /** Linear constructor.
  117.      * <p>Build a PVCoordinates from two other ones and corresponding scale factors.</p>
  118.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2</p>
  119.      * @param a1 first scale factor
  120.      * @param pv1 first base (unscaled) PVCoordinates
  121.      * @param a2 second scale factor
  122.      * @param pv2 second base (unscaled) PVCoordinates
  123.      */
  124.     public PVCoordinates(final double a1, final PVCoordinates pv1,
  125.                          final double a2, final PVCoordinates pv2) {
  126.         position     = new Vector3D(a1, pv1.position,     a2, pv2.position);
  127.         velocity     = new Vector3D(a1, pv1.velocity,     a2, pv2.velocity);
  128.         acceleration = new Vector3D(a1, pv1.acceleration, a2, pv2.acceleration);
  129.     }

  131.     /** Linear constructor.
  132.      * <p>Build a PVCoordinates from three other ones and corresponding scale factors.</p>
  133.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3</p>
  134.      * @param a1 first scale factor
  135.      * @param pv1 first base (unscaled) PVCoordinates
  136.      * @param a2 second scale factor
  137.      * @param pv2 second base (unscaled) PVCoordinates
  138.      * @param a3 third scale factor
  139.      * @param pv3 third base (unscaled) PVCoordinates
  140.      */
  141.     public PVCoordinates(final double a1, final PVCoordinates pv1,
  142.                          final double a2, final PVCoordinates pv2,
  143.                          final double a3, final PVCoordinates pv3) {
  144.         position     = new Vector3D(a1, pv1.position,     a2, pv2.position,     a3, pv3.position);
  145.         velocity     = new Vector3D(a1, pv1.velocity,     a2, pv2.velocity,     a3, pv3.velocity);
  146.         acceleration = new Vector3D(a1, pv1.acceleration, a2, pv2.acceleration, a3, pv3.acceleration);
  147.     }

  149.     /** Linear constructor.
  150.      * <p>Build a PVCoordinates from four other ones and corresponding scale factors.</p>
  151.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4</p>
  152.      * @param a1 first scale factor
  153.      * @param pv1 first base (unscaled) PVCoordinates
  154.      * @param a2 second scale factor
  155.      * @param pv2 second base (unscaled) PVCoordinates
  156.      * @param a3 third scale factor
  157.      * @param pv3 third base (unscaled) PVCoordinates
  158.      * @param a4 fourth scale factor
  159.      * @param pv4 fourth base (unscaled) PVCoordinates
  160.      */
  161.     public PVCoordinates(final double a1, final PVCoordinates pv1,
  162.                          final double a2, final PVCoordinates pv2,
  163.                          final double a3, final PVCoordinates pv3,
  164.                          final double a4, final PVCoordinates pv4) {
  165.         position     = new Vector3D(a1, pv1.position,     a2, pv2.position,
  166.                                     a3, pv3.position,     a4, pv4.position);
  167.         velocity     = new Vector3D(a1, pv1.velocity,     a2, pv2.velocity,
  168.                                     a3, pv3.velocity,     a4, pv4.velocity);
  169.         acceleration = new Vector3D(a1, pv1.acceleration, a2, pv2.acceleration,
  170.                                     a3, pv3.acceleration, a4, pv4.acceleration);
  171.     }

  173.     /** Builds a PVCoordinates triplet from  a {@link FieldVector3D}&lt;{@link Derivative}&gt;.
  174.      * <p>
  175.      * The vector components must have time as their only derivation parameter and
  176.      * have consistent derivation orders.
  177.      * </p>
  178.      * @param p vector with time-derivatives embedded within the coordinates
  179.      * @param <U> type of the derivative
  180.      */
  181.     public <U extends Derivative<U>> PVCoordinates(final FieldVector3D<U> p) {
  182.         position = new Vector3D(p.getX().getReal(), p.getY().getReal(), p.getZ().getReal());
  183.         if (p.getX().getOrder() >= 1) {
  184.             velocity = new Vector3D(p.getX().getPartialDerivative(1),
  185.                                     p.getY().getPartialDerivative(1),
  186.                                     p.getZ().getPartialDerivative(1));
  187.             if (p.getX().getOrder() >= 2) {
  188.                 acceleration = new Vector3D(p.getX().getPartialDerivative(2),
  189.                                             p.getY().getPartialDerivative(2),
  190.                                             p.getZ().getPartialDerivative(2));
  191.             } else {
  192.                 acceleration = Vector3D.ZERO;
  193.             }
  194.         } else {
  195.             velocity     = Vector3D.ZERO;
  196.             acceleration = Vector3D.ZERO;
  197.         }
  198.     }

  200.     /**
  201.      * Builds PV coordinates with the givne position, zero velocity, and zero
  202.      * acceleration.
  203.      *
  204.      * @param position position vector (m)
  205.      */
  206.     public PVCoordinates(final Vector3D position) {
  207.         this(position, Vector3D.ZERO);
  208.     }

  210.     /** Transform the instance to a {@link FieldVector3D}&lt;{@link DerivativeStructure}&gt;.
  211.      * <p>
  212.      * The {@link DerivativeStructure} coordinates correspond to time-derivatives up
  213.      * to the user-specified order.
  214.      * </p>
  215.      * @param order derivation order for the vector components (must be either 0, 1 or 2)
  216.      * @return vector with time-derivatives embedded within the coordinates
  217.      */
  218.     public FieldVector3D<DerivativeStructure> toDerivativeStructureVector(final int order) {

  220.         final DSFactory factory;
  221.         final DerivativeStructure x;
  222.         final DerivativeStructure y;
  223.         final DerivativeStructure z;
  224.         switch (order) {
  225.             case 0 :
  226.                 factory = new DSFactory(1, order);
  227.                 x = factory.build(position.getX());
  228.                 y = factory.build(position.getY());
  229.                 z = factory.build(position.getZ());
  230.                 break;
  231.             case 1 :
  232.                 factory = new DSFactory(1, order);
  233.                 x = factory.build(position.getX(), velocity.getX());
  234.                 y = factory.build(position.getY(), velocity.getY());
  235.                 z = factory.build(position.getZ(), velocity.getZ());
  236.                 break;
  237.             case 2 :
  238.                 factory = new DSFactory(1, order);
  239.                 x = factory.build(position.getX(), velocity.getX(), acceleration.getX());
  240.                 y = factory.build(position.getY(), velocity.getY(), acceleration.getY());
  241.                 z = factory.build(position.getZ(), velocity.getZ(), acceleration.getZ());
  242.                 break;
  243.             default :
  244.                 throw new OrekitException(OrekitMessages.OUT_OF_RANGE_DERIVATION_ORDER, order);
  245.         }

  247.         return new FieldVector3D<>(x, y, z);

  249.     }

  251.     /** Transform the instance to a {@link FieldVector3D}&lt;{@link UnivariateDerivative1}&gt;.
  252.      * <p>
  253.      * The {@link UnivariateDerivative1} coordinates correspond to time-derivatives up
  254.      * to the order 1.
  255.      * </p>
  256.      * @return vector with time-derivatives embedded within the coordinates
  257.      * @see #toUnivariateDerivative2Vector()
  258.      * @since 10.2
  259.      */
  260.     public FieldVector3D<UnivariateDerivative1> toUnivariateDerivative1Vector() {

  262.         final UnivariateDerivative1 x = new UnivariateDerivative1(position.getX(), velocity.getX());
  263.         final UnivariateDerivative1 y = new UnivariateDerivative1(position.getY(), velocity.getY());
  264.         final UnivariateDerivative1 z = new UnivariateDerivative1(position.getZ(), velocity.getZ());

  266.         return new FieldVector3D<>(x, y, z);
  267.     }

  269.     /** Transform the instance to a {@link FieldVector3D}&lt;{@link UnivariateDerivative2}&gt;.
  270.      * <p>
  271.      * The {@link UnivariateDerivative2} coordinates correspond to time-derivatives up
  272.      * to the order 2.
  273.      * </p>
  274.      * @return vector with time-derivatives embedded within the coordinates
  275.      * @see #toUnivariateDerivative1Vector()
  276.      * @since 10.2
  277.      */
  278.     public FieldVector3D<UnivariateDerivative2> toUnivariateDerivative2Vector() {

  280.         final UnivariateDerivative2 x = new UnivariateDerivative2(position.getX(), velocity.getX(), acceleration.getX());
  281.         final UnivariateDerivative2 y = new UnivariateDerivative2(position.getY(), velocity.getY(), acceleration.getY());
  282.         final UnivariateDerivative2 z = new UnivariateDerivative2(position.getZ(), velocity.getZ(), acceleration.getZ());

  284.         return new FieldVector3D<>(x, y, z);
  285.     }

  287.     /** Transform the instance to a {@link FieldPVCoordinates}&lt;{@link DerivativeStructure}&gt;.
  288.      * <p>
  289.      * The {@link DerivativeStructure} coordinates correspond to time-derivatives up
  290.      * to the user-specified order. As both the instance components {@link #getPosition() position},
  291.      * {@link #getVelocity() velocity} and {@link #getAcceleration() acceleration} and the
  292.      * {@link DerivativeStructure#getPartialDerivative(int...) derivatives} of the components
  293.      * holds time-derivatives, there are several ways to retrieve these derivatives. If for example
  294.      * the {@code order} is set to 2, then both {@code pv.getPosition().getX().getPartialDerivative(2)},
  295.      * {@code pv.getVelocity().getX().getPartialDerivative(1)} and
  296.      * {@code pv.getAcceleration().getX().getValue()} return the exact same value.
  297.      * </p>
  298.      * <p>
  299.      * If derivation order is 1, the first derivative of acceleration will be computed as a
  300.      * Keplerian-only jerk. If derivation order is 2, the second derivative of velocity (which
  301.      * is also the first derivative of acceleration) will be computed as a Keplerian-only jerk,
  302.      * and the second derivative of acceleration will be computed as a Keplerian-only jounce.
  303.      * </p>
  304.      * @param order derivation order for the vector components (must be either 0, 1 or 2)
  305.      * @return pv coordinates with time-derivatives embedded within the coordinates
  306.      * @since 9.2
  307.      */
  308.     public FieldPVCoordinates<DerivativeStructure> toDerivativeStructurePV(final int order) {

  310.         final DSFactory factory;
  311.         final DerivativeStructure x0;
  312.         final DerivativeStructure y0;
  313.         final DerivativeStructure z0;
  314.         final DerivativeStructure x1;
  315.         final DerivativeStructure y1;
  316.         final DerivativeStructure z1;
  317.         final DerivativeStructure x2;
  318.         final DerivativeStructure y2;
  319.         final DerivativeStructure z2;
  320.         switch (order) {
  321.             case 0 :
  322.                 factory = new DSFactory(1, order);
  323.                 x0 = factory.build(position.getX());
  324.                 y0 = factory.build(position.getY());
  325.                 z0 = factory.build(position.getZ());
  326.                 x1 = factory.build(velocity.getX());
  327.                 y1 = factory.build(velocity.getY());
  328.                 z1 = factory.build(velocity.getZ());
  329.                 x2 = factory.build(acceleration.getX());
  330.                 y2 = factory.build(acceleration.getY());
  331.                 z2 = factory.build(acceleration.getZ());
  332.                 break;
  333.             case 1 : {
  334.                 factory = new DSFactory(1, order);
  335.                 final double   r2            = position.getNormSq();
  336.                 final double   r             = FastMath.sqrt(r2);
  337.                 final double   pvOr2         = Vector3D.dotProduct(position, velocity) / r2;
  338.                 final double   a             = acceleration.getNorm();
  339.                 final double   aOr           = a / r;
  340.                 final Vector3D keplerianJerk = new Vector3D(-3 * pvOr2, acceleration, -aOr, velocity);
  341.                 x0 = factory.build(position.getX(),     velocity.getX());
  342.                 y0 = factory.build(position.getY(),     velocity.getY());
  343.                 z0 = factory.build(position.getZ(),     velocity.getZ());
  344.                 x1 = factory.build(velocity.getX(),     acceleration.getX());
  345.                 y1 = factory.build(velocity.getY(),     acceleration.getY());
  346.                 z1 = factory.build(velocity.getZ(),     acceleration.getZ());
  347.                 x2 = factory.build(acceleration.getX(), keplerianJerk.getX());
  348.                 y2 = factory.build(acceleration.getY(), keplerianJerk.getY());
  349.                 z2 = factory.build(acceleration.getZ(), keplerianJerk.getZ());
  350.                 break;
  351.             }
  352.             case 2 : {
  353.                 factory = new DSFactory(1, order);
  354.                 final double   r2              = position.getNormSq();
  355.                 final double   r               = FastMath.sqrt(r2);
  356.                 final double   pvOr2           = Vector3D.dotProduct(position, velocity) / r2;
  357.                 final double   a               = acceleration.getNorm();
  358.                 final double   aOr             = a / r;
  359.                 final Vector3D keplerianJerk   = new Vector3D(-3 * pvOr2, acceleration, -aOr, velocity);
  360.                 final double   v2              = velocity.getNormSq();
  361.                 final double   pa              = Vector3D.dotProduct(position, acceleration);
  362.                 final double   aj              = Vector3D.dotProduct(acceleration, keplerianJerk);
  363.                 final Vector3D keplerianJounce = new Vector3D(-3 * (v2 + pa) / r2 + 15 * pvOr2 * pvOr2 - aOr, acceleration,
  364.                                                               4 * aOr * pvOr2 - aj / (a * r), velocity);
  365.                 x0 = factory.build(position.getX(),     velocity.getX(),      acceleration.getX());
  366.                 y0 = factory.build(position.getY(),     velocity.getY(),      acceleration.getY());
  367.                 z0 = factory.build(position.getZ(),     velocity.getZ(),      acceleration.getZ());
  368.                 x1 = factory.build(velocity.getX(),     acceleration.getX(),  keplerianJerk.getX());
  369.                 y1 = factory.build(velocity.getY(),     acceleration.getY(),  keplerianJerk.getY());
  370.                 z1 = factory.build(velocity.getZ(),     acceleration.getZ(),  keplerianJerk.getZ());
  371.                 x2 = factory.build(acceleration.getX(), keplerianJerk.getX(), keplerianJounce.getX());
  372.                 y2 = factory.build(acceleration.getY(), keplerianJerk.getY(), keplerianJounce.getY());
  373.                 z2 = factory.build(acceleration.getZ(), keplerianJerk.getZ(), keplerianJounce.getZ());
  374.                 break;
  375.             }
  376.             default :
  377.                 throw new OrekitException(OrekitMessages.OUT_OF_RANGE_DERIVATION_ORDER, order);
  378.         }

  380.         return new FieldPVCoordinates<>(new FieldVector3D<>(x0, y0, z0),
  381.                                         new FieldVector3D<>(x1, y1, z1),
  382.                                         new FieldVector3D<>(x2, y2, z2));

  384.     }

  386.     /** Transform the instance to a {@link FieldPVCoordinates}&lt;{@link UnivariateDerivative1}&gt;.
  387.      * <p>
  388.      * The {@link UnivariateDerivative1} coordinates correspond to time-derivatives up
  389.      * to the order 1.
  390.      * The first derivative of acceleration will be computed as a Keplerian-only jerk.
  391.      * </p>
  392.      * @return pv coordinates with time-derivatives embedded within the coordinates
  393.      * @since 10.2
  394.      */
  395.     public FieldPVCoordinates<UnivariateDerivative1> toUnivariateDerivative1PV() {

  397.         final double   r2            = position.getNormSq();
  398.         final double   r             = FastMath.sqrt(r2);
  399.         final double   pvOr2         = Vector3D.dotProduct(position, velocity) / r2;
  400.         final double   a             = acceleration.getNorm();
  401.         final double   aOr           = a / r;
  402.         final Vector3D keplerianJerk = new Vector3D(-3 * pvOr2, acceleration, -aOr, velocity);

  404.         final UnivariateDerivative1 x0 = new UnivariateDerivative1(position.getX(),     velocity.getX());
  405.         final UnivariateDerivative1 y0 = new UnivariateDerivative1(position.getY(),     velocity.getY());
  406.         final UnivariateDerivative1 z0 = new UnivariateDerivative1(position.getZ(),     velocity.getZ());
  407.         final UnivariateDerivative1 x1 = new UnivariateDerivative1(velocity.getX(),     acceleration.getX());
  408.         final UnivariateDerivative1 y1 = new UnivariateDerivative1(velocity.getY(),     acceleration.getY());
  409.         final UnivariateDerivative1 z1 = new UnivariateDerivative1(velocity.getZ(),     acceleration.getZ());
  410.         final UnivariateDerivative1 x2 = new UnivariateDerivative1(acceleration.getX(), keplerianJerk.getX());
  411.         final UnivariateDerivative1 y2 = new UnivariateDerivative1(acceleration.getY(), keplerianJerk.getY());
  412.         final UnivariateDerivative1 z2 = new UnivariateDerivative1(acceleration.getZ(), keplerianJerk.getZ());

  414.         return new FieldPVCoordinates<>(new FieldVector3D<>(x0, y0, z0),
  415.                                         new FieldVector3D<>(x1, y1, z1),
  416.                                         new FieldVector3D<>(x2, y2, z2));

  418.     }

  420.     /** Transform the instance to a {@link FieldPVCoordinates}&lt;{@link UnivariateDerivative2}&gt;.
  421.      * <p>
  422.      * The {@link UnivariateDerivative2} coordinates correspond to time-derivatives up
  423.      * to the order 2.
  424.      * As derivation order is 2, the second derivative of velocity (which
  425.      * is also the first derivative of acceleration) will be computed as a Keplerian-only jerk,
  426.      * and the second derivative of acceleration will be computed as a Keplerian-only jounce.
  427.      * </p>
  428.      * @return pv coordinates with time-derivatives embedded within the coordinates
  429.      * @since 10.2
  430.      */
  431.     public FieldPVCoordinates<UnivariateDerivative2> toUnivariateDerivative2PV() {

  433.         final double   r2              = position.getNormSq();
  434.         final double   r               = FastMath.sqrt(r2);
  435.         final double   pvOr2           = Vector3D.dotProduct(position, velocity) / r2;
  436.         final double   a               = acceleration.getNorm();
  437.         final double   aOr             = a / r;
  438.         final Vector3D keplerianJerk   = new Vector3D(-3 * pvOr2, acceleration, -aOr, velocity);
  439.         final double   v2              = velocity.getNormSq();
  440.         final double   pa              = Vector3D.dotProduct(position, acceleration);
  441.         final double   aj              = Vector3D.dotProduct(acceleration, keplerianJerk);
  442.         final Vector3D keplerianJounce = new Vector3D(-3 * (v2 + pa) / r2 + 15 * pvOr2 * pvOr2 - aOr, acceleration,
  443.                                                       4 * aOr * pvOr2 - aj / (a * r), velocity);

  445.         final UnivariateDerivative2 x0 = new UnivariateDerivative2(position.getX(),     velocity.getX(),      acceleration.getX());
  446.         final UnivariateDerivative2 y0 = new UnivariateDerivative2(position.getY(),     velocity.getY(),      acceleration.getY());
  447.         final UnivariateDerivative2 z0 = new UnivariateDerivative2(position.getZ(),     velocity.getZ(),      acceleration.getZ());
  448.         final UnivariateDerivative2 x1 = new UnivariateDerivative2(velocity.getX(),     acceleration.getX(),  keplerianJerk.getX());
  449.         final UnivariateDerivative2 y1 = new UnivariateDerivative2(velocity.getY(),     acceleration.getY(),  keplerianJerk.getY());
  450.         final UnivariateDerivative2 z1 = new UnivariateDerivative2(velocity.getZ(),     acceleration.getZ(),  keplerianJerk.getZ());
  451.         final UnivariateDerivative2 x2 = new UnivariateDerivative2(acceleration.getX(), keplerianJerk.getX(), keplerianJounce.getX());
  452.         final UnivariateDerivative2 y2 = new UnivariateDerivative2(acceleration.getY(), keplerianJerk.getY(), keplerianJounce.getY());
  453.         final UnivariateDerivative2 z2 = new UnivariateDerivative2(acceleration.getZ(), keplerianJerk.getZ(), keplerianJounce.getZ());

  455.         return new FieldPVCoordinates<>(new FieldVector3D<>(x0, y0, z0),
  456.                                         new FieldVector3D<>(x1, y1, z1),
  457.                                         new FieldVector3D<>(x2, y2, z2));

  459.     }

  461.     /** Estimate velocity between two positions.
  462.      * <p>Estimation is based on a simple fixed velocity translation
  463.      * during the time interval between the two positions.</p>
  464.      * @param start start position
  465.      * @param end end position
  466.      * @param dt time elapsed between the dates of the two positions
  467.      * @return velocity allowing to go from start to end positions
  468.      */
  469.     public static Vector3D estimateVelocity(final Vector3D start, final Vector3D end, final double dt) {
  470.         final double scale = 1.0 / dt;
  471.         return new Vector3D(scale, end, -scale, start);
  472.     }

  474.     /** Get a time-shifted state.
  475.      * <p>
  476.      * The state can be slightly shifted to close dates. This shift is based on
  477.      * a simple Taylor expansion. It is <em>not</em> intended as a replacement for
  478.      * proper orbit propagation (it is not even Keplerian!) but should be sufficient
  479.      * for either small time shifts or coarse accuracy.
  480.      * </p>
  481.      * @param dt time shift in seconds
  482.      * @return a new state, shifted with respect to the instance (which is immutable)
  483.      */
  484.     public PVCoordinates shiftedBy(final double dt) {
  485.         return new PVCoordinates(positionShiftedBy(dt),
  486.                                  new Vector3D(1, velocity, dt, acceleration),
  487.                                  acceleration);
  488.     }

  490.     /**
  491.      * Get a time-shifted position. Same as {@link #shiftedBy(double)} except
  492.      * that only the sifted position is returned.
  493.      * <p>
  494.      * The state can be slightly shifted to close dates. This shift is based on
  495.      * a simple Taylor expansion. It is <em>not</em> intended as a replacement
  496.      * for proper orbit propagation (it is not even Keplerian!) but should be
  497.      * sufficient for either small time shifts or coarse accuracy.
  498.      * </p>
  499.      *
  500.      * @param dt time shift in seconds
  501.      * @return a new state, shifted with respect to the instance (which is
  502.      * immutable)
  503.      */
  504.     public Vector3D positionShiftedBy(final double dt) {
  505.         return new Vector3D(1, position, dt, velocity, 0.5 * dt * dt, acceleration);
  506.     }

  508.     /** Gets the position.
  509.      * @return the position vector (m).
  510.      */
  511.     public Vector3D getPosition() {
  512.         return position;
  513.     }

  515.     /** Gets the velocity.
  516.      * @return the velocity vector (m/s).
  517.      */
  518.     public Vector3D getVelocity() {
  519.         return velocity;
  520.     }

  522.     /** Gets the acceleration.
  523.      * @return the acceleration vector (m/s²).
  524.      */
  525.     public Vector3D getAcceleration() {
  526.         return acceleration;
  527.     }

  529.     /** Gets the momentum.
  530.      * <p>This vector is the p &otimes; v where p is position, v is velocity
  531.      * and &otimes; is cross product. To get the real physical angular momentum
  532.      * you need to multiply this vector by the mass.</p>
  533.      * <p>The returned vector is recomputed each time this method is called, it
  534.      * is not cached.</p>
  535.      * @return a new instance of the momentum vector (m²/s).
  536.      */
  537.     public Vector3D getMomentum() {
  538.         return Vector3D.crossProduct(position, velocity);
  539.     }

  541.     /**
  542.      * Get the angular velocity (spin) of this point as seen from the origin.
  543.      *
  544.      * <p> The angular velocity vector is parallel to the {@link #getMomentum()
  545.      * angular momentum} and is computed by ω = p &times; v / ||p||²
  546.      *
  547.      * @return the angular velocity vector
  548.      * @see <a href="http://en.wikipedia.org/wiki/Angular_velocity">Angular Velocity on
  549.      *      Wikipedia</a>
  550.      */
  551.     public Vector3D getAngularVelocity() {
  552.         return this.getMomentum().scalarMultiply(1.0 / this.getPosition().getNormSq());
  553.     }

  555.     /** Get the opposite of the instance.
  556.      * @return a new position-velocity which is opposite to the instance
  557.      */
  558.     public PVCoordinates negate() {
  559.         return new PVCoordinates(position.negate(), velocity.negate(), acceleration.negate());
  560.     }

  562.     /** Normalize the position part of the instance.
  563.      * <p>
  564.      * The computed coordinates first component (position) will be a
  565.      * normalized vector, the second component (velocity) will be the
  566.      * derivative of the first component (hence it will generally not
  567.      * be normalized), and the third component (acceleration) will be the
  568.      * derivative of the second component (hence it will generally not
  569.      * be normalized).
  570.      * </p>
  571.      * @return a new instance, with first component normalized and
  572.      * remaining component computed to have consistent derivatives
  573.      */
  574.     public PVCoordinates normalize() {
  575.         final double   inv     = 1.0 / position.getNorm();
  576.         final Vector3D u       = new Vector3D(inv, position);
  577.         final Vector3D v       = new Vector3D(inv, velocity);
  578.         final Vector3D w       = new Vector3D(inv, acceleration);
  579.         final double   uv      = Vector3D.dotProduct(u, v);
  580.         final double   v2      = Vector3D.dotProduct(v, v);
  581.         final double   uw      = Vector3D.dotProduct(u, w);
  582.         final Vector3D uDot    = new Vector3D(1, v, -uv, u);
  583.         final Vector3D uDotDot = new Vector3D(1, w, -2 * uv, v, 3 * uv * uv - v2 - uw, u);
  584.         return new PVCoordinates(u, uDot, uDotDot);
  585.     }

  587.     /** Compute the cross-product of two instances.
  588.      * @param pv1 first instances
  589.      * @param pv2 second instances
  590.      * @return the cross product v1 ^ v2 as a new instance
  591.      */
  592.     public static PVCoordinates crossProduct(final PVCoordinates pv1, final PVCoordinates pv2) {
  593.         final Vector3D p1 = pv1.position;
  594.         final Vector3D v1 = pv1.velocity;
  595.         final Vector3D a1 = pv1.acceleration;
  596.         final Vector3D p2 = pv2.position;
  597.         final Vector3D v2 = pv2.velocity;
  598.         final Vector3D a2 = pv2.acceleration;
  599.         return new PVCoordinates(Vector3D.crossProduct(p1, p2),
  600.                                  new Vector3D(1, Vector3D.crossProduct(p1, v2),
  601.                                               1, Vector3D.crossProduct(v1, p2)),
  602.                                  new Vector3D(1, Vector3D.crossProduct(p1, a2),
  603.                                               2, Vector3D.crossProduct(v1, v2),
  604.                                               1, Vector3D.crossProduct(a1, p2)));
  605.     }

  607.     /** Return a string representation of this position/velocity pair.
  608.      * @return string representation of this position/velocity pair
  609.      */
  610.     public String toString() {
  611.         final String comma = ", ";
  612.         return new StringBuilder().append('{').append("P(").
  613.                 append(position.getX()).append(comma).
  614.                 append(position.getY()).append(comma).
  615.                 append(position.getZ()).append("), V(").
  616.                 append(velocity.getX()).append(comma).
  617.                 append(velocity.getY()).append(comma).
  618.                 append(velocity.getZ()).append("), A(").
  619.                 append(acceleration.getX()).append(comma).
  620.                 append(acceleration.getY()).append(comma).
  621.                 append(acceleration.getZ()).append(")}").toString();
  622.     }

  624.     /** {@inheritDoc} */
  625.     @Override
  626.     public PVCoordinates blendArithmeticallyWith(final PVCoordinates other, final double blendingValue)
  627.             throws MathIllegalArgumentException {
  628.         final Vector3D blendedPosition     = position.blendArithmeticallyWith(other.position, blendingValue);
  629.         final Vector3D blendedVelocity     = velocity.blendArithmeticallyWith(other.velocity, blendingValue);
  630.         final Vector3D blendedAcceleration = acceleration.blendArithmeticallyWith(other.acceleration, blendingValue);

  632.         return new PVCoordinates(blendedPosition, blendedVelocity, blendedAcceleration);
  633.     }

  635. }
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