PVCoordinates.java

  1. /* Copyright 2002-2020 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 java.io.Serializable;

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

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

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

  51.     /** Serializable UID. */
  52.     private static final long serialVersionUID = 20140407L;

  54.     /** The position. */
  55.     private final Vector3D position;

  57.     /** The velocity. */
  58.     private final Vector3D velocity;

  60.     /** The acceleration. */
  61.     private final Vector3D acceleration;

  63.     /** Simple constructor.
  64.      * <p> Set the Coordinates to default : (0 0 0), (0 0 0), (0 0 0).</p>
  65.      */
  66.     public PVCoordinates() {
  67.         position     = Vector3D.ZERO;
  68.         velocity     = Vector3D.ZERO;
  69.         acceleration = Vector3D.ZERO;
  70.     }

  72.     /** Builds a PVCoordinates triplet with zero acceleration.
  73.      * <p>Acceleration is set to zero</p>
  74.      * @param position the position vector (m)
  75.      * @param velocity the velocity vector (m/s)
  76.      */
  77.     public PVCoordinates(final Vector3D position, final Vector3D velocity) {
  78.         this.position     = position;
  79.         this.velocity     = velocity;
  80.         this.acceleration = Vector3D.ZERO;
  81.     }

  83.     /** Builds a PVCoordinates triplet.
  84.      * @param position the position vector (m)
  85.      * @param velocity the velocity vector (m/s)
  86.      * @param acceleration the acceleration vector (m/s²)
  87.      */
  88.     public PVCoordinates(final Vector3D position, final Vector3D velocity, final Vector3D acceleration) {
  89.         this.position     = position;
  90.         this.velocity     = velocity;
  91.         this.acceleration = acceleration;
  92.     }

  94.     /** Multiplicative constructor.
  95.      * <p>Build a PVCoordinates from another one and a scale factor.</p>
  96.      * <p>The PVCoordinates built will be a * pv</p>
  97.      * @param a scale factor
  98.      * @param pv base (unscaled) PVCoordinates
  99.      */
  100.     public PVCoordinates(final double a, final PVCoordinates pv) {
  101.         position     = new Vector3D(a, pv.position);
  102.         velocity     = new Vector3D(a, pv.velocity);
  103.         acceleration = new Vector3D(a, pv.acceleration);
  104.     }

  106.     /** Subtractive constructor.
  107.      * <p>Build a relative PVCoordinates from a start and an end position.</p>
  108.      * <p>The PVCoordinates built will be end - start.</p>
  109.      * @param start Starting PVCoordinates
  110.      * @param end ending PVCoordinates
  111.      */
  112.     public PVCoordinates(final PVCoordinates start, final PVCoordinates end) {
  113.         this.position     = end.position.subtract(start.position);
  114.         this.velocity     = end.velocity.subtract(start.velocity);
  115.         this.acceleration = end.acceleration.subtract(start.acceleration);
  116.     }

  118.     /** Linear constructor.
  119.      * <p>Build a PVCoordinates from two other ones and corresponding scale factors.</p>
  120.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2</p>
  121.      * @param a1 first scale factor
  122.      * @param pv1 first base (unscaled) PVCoordinates
  123.      * @param a2 second scale factor
  124.      * @param pv2 second base (unscaled) PVCoordinates
  125.      */
  126.     public PVCoordinates(final double a1, final PVCoordinates pv1,
  127.                          final double a2, final PVCoordinates pv2) {
  128.         position     = new Vector3D(a1, pv1.position,     a2, pv2.position);
  129.         velocity     = new Vector3D(a1, pv1.velocity,     a2, pv2.velocity);
  130.         acceleration = new Vector3D(a1, pv1.acceleration, a2, pv2.acceleration);
  131.     }

  133.     /** Linear constructor.
  134.      * <p>Build a PVCoordinates from three other ones and corresponding scale factors.</p>
  135.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3</p>
  136.      * @param a1 first scale factor
  137.      * @param pv1 first base (unscaled) PVCoordinates
  138.      * @param a2 second scale factor
  139.      * @param pv2 second base (unscaled) PVCoordinates
  140.      * @param a3 third scale factor
  141.      * @param pv3 third base (unscaled) PVCoordinates
  142.      */
  143.     public PVCoordinates(final double a1, final PVCoordinates pv1,
  144.                          final double a2, final PVCoordinates pv2,
  145.                          final double a3, final PVCoordinates pv3) {
  146.         position     = new Vector3D(a1, pv1.position,     a2, pv2.position,     a3, pv3.position);
  147.         velocity     = new Vector3D(a1, pv1.velocity,     a2, pv2.velocity,     a3, pv3.velocity);
  148.         acceleration = new Vector3D(a1, pv1.acceleration, a2, pv2.acceleration, a3, pv3.acceleration);
  149.     }

  151.     /** Linear constructor.
  152.      * <p>Build a PVCoordinates from four other ones and corresponding scale factors.</p>
  153.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4</p>
  154.      * @param a1 first scale factor
  155.      * @param pv1 first base (unscaled) PVCoordinates
  156.      * @param a2 second scale factor
  157.      * @param pv2 second base (unscaled) PVCoordinates
  158.      * @param a3 third scale factor
  159.      * @param pv3 third base (unscaled) PVCoordinates
  160.      * @param a4 fourth scale factor
  161.      * @param pv4 fourth base (unscaled) PVCoordinates
  162.      */
  163.     public PVCoordinates(final double a1, final PVCoordinates pv1,
  164.                          final double a2, final PVCoordinates pv2,
  165.                          final double a3, final PVCoordinates pv3,
  166.                          final double a4, final PVCoordinates pv4) {
  167.         position     = new Vector3D(a1, pv1.position,     a2, pv2.position,
  168.                                     a3, pv3.position,     a4, pv4.position);
  169.         velocity     = new Vector3D(a1, pv1.velocity,     a2, pv2.velocity,
  170.                                     a3, pv3.velocity,     a4, pv4.velocity);
  171.         acceleration = new Vector3D(a1, pv1.acceleration, a2, pv2.acceleration,
  172.                                     a3, pv3.acceleration, a4, pv4.acceleration);
  173.     }

  175.     /** Builds a PVCoordinates triplet from  a {@link FieldVector3D}&lt;{@link DerivativeStructure}&gt;.
  176.      * <p>
  177.      * The vector components must have time as their only derivation parameter and
  178.      * have consistent derivation orders.
  179.      * </p>
  180.      * @param p vector with time-derivatives embedded within the coordinates
  181.      */
  182.     public PVCoordinates(final FieldVector3D<DerivativeStructure> p) {
  183.         position = new Vector3D(p.getX().getReal(), p.getY().getReal(), p.getZ().getReal());
  184.         if (p.getX().getOrder() >= 1) {
  185.             velocity = new Vector3D(p.getX().getPartialDerivative(1),
  186.                                     p.getY().getPartialDerivative(1),
  187.                                     p.getZ().getPartialDerivative(1));
  188.             if (p.getX().getOrder() >= 2) {
  189.                 acceleration = new Vector3D(p.getX().getPartialDerivative(2),
  190.                                             p.getY().getPartialDerivative(2),
  191.                                             p.getZ().getPartialDerivative(2));
  192.             } else {
  193.                 acceleration = Vector3D.ZERO;
  194.             }
  195.         } else {
  196.             velocity     = Vector3D.ZERO;
  197.             acceleration = Vector3D.ZERO;
  198.         }
  199.     }

  201.     /** Transform the instance to a {@link FieldVector3D}&lt;{@link DerivativeStructure}&gt;.
  202.      * <p>
  203.      * The {@link DerivativeStructure} coordinates correspond to time-derivatives up
  204.      * to the user-specified order.
  205.      * </p>
  206.      * @param order derivation order for the vector components (must be either 0, 1 or 2)
  207.      * @return vector with time-derivatives embedded within the coordinates
  208.      */
  209.     public FieldVector3D<DerivativeStructure> toDerivativeStructureVector(final int order) {

  211.         final DSFactory factory;
  212.         final DerivativeStructure x;
  213.         final DerivativeStructure y;
  214.         final DerivativeStructure z;
  215.         switch(order) {
  216.             case 0 :
  217.                 factory = new DSFactory(1, order);
  218.                 x = factory.build(position.getX());
  219.                 y = factory.build(position.getY());
  220.                 z = factory.build(position.getZ());
  221.                 break;
  222.             case 1 :
  223.                 factory = new DSFactory(1, order);
  224.                 x = factory.build(position.getX(), velocity.getX());
  225.                 y = factory.build(position.getY(), velocity.getY());
  226.                 z = factory.build(position.getZ(), velocity.getZ());
  227.                 break;
  228.             case 2 :
  229.                 factory = new DSFactory(1, order);
  230.                 x = factory.build(position.getX(), velocity.getX(), acceleration.getX());
  231.                 y = factory.build(position.getY(), velocity.getY(), acceleration.getY());
  232.                 z = factory.build(position.getZ(), velocity.getZ(), acceleration.getZ());
  233.                 break;
  234.             default :
  235.                 throw new OrekitException(OrekitMessages.OUT_OF_RANGE_DERIVATION_ORDER, order);
  236.         }

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

  240.     }

  242.     /** Transform the instance to a {@link FieldVector3D}&lt;{@link UnivariateDerivative1}&gt;.
  243.      * <p>
  244.      * The {@link UnivariateDerivative1} coordinates correspond to time-derivatives up
  245.      * to the order 1.
  246.      * </p>
  247.      * @return vector with time-derivatives embedded within the coordinates
  248.      * @see #toUnivariateDerivative2Vector()
  249.      * @since 10.2
  250.      */
  251.     public FieldVector3D<UnivariateDerivative1> toUnivariateDerivative1Vector() {

  253.         final UnivariateDerivative1 x = new UnivariateDerivative1(position.getX(), velocity.getX());
  254.         final UnivariateDerivative1 y = new UnivariateDerivative1(position.getY(), velocity.getY());
  255.         final UnivariateDerivative1 z = new UnivariateDerivative1(position.getZ(), velocity.getZ());

  257.         return new FieldVector3D<>(x, y, z);
  258.     }

  260.     /** Transform the instance to a {@link FieldVector3D}&lt;{@link UnivariateDerivative2}&gt;.
  261.      * <p>
  262.      * The {@link UnivariateDerivative2} coordinates correspond to time-derivatives up
  263.      * to the order 2.
  264.      * </p>
  265.      * @return vector with time-derivatives embedded within the coordinates
  266.      * @see #toUnivariateDerivative1Vector()
  267.      * @since 10.2
  268.      */
  269.     public FieldVector3D<UnivariateDerivative2> toUnivariateDerivative2Vector() {

  271.         final UnivariateDerivative2 x = new UnivariateDerivative2(position.getX(), velocity.getX(), acceleration.getX());
  272.         final UnivariateDerivative2 y = new UnivariateDerivative2(position.getY(), velocity.getY(), acceleration.getY());
  273.         final UnivariateDerivative2 z = new UnivariateDerivative2(position.getZ(), velocity.getZ(), acceleration.getZ());

  275.         return new FieldVector3D<>(x, y, z);
  276.     }

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

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

  371.         return new FieldPVCoordinates<>(new FieldVector3D<>(x0, y0, z0),
  372.                                         new FieldVector3D<>(x1, y1, z1),
  373.                                         new FieldVector3D<>(x2, y2, z2));

  375.     }

  377.     /** Transform the instance to a {@link FieldPVCoordinates}&lt;{@link UnivariateDerivative1}&gt;.
  378.      * <p>
  379.      * The {@link UnivariateDerivative1} coordinates correspond to time-derivatives up
  380.      * to the order 1.
  381.      * The first derivative of acceleration will be computed as a Keplerian-only jerk.
  382.      * </p>
  383.      * @return pv coordinates with time-derivatives embedded within the coordinates
  384.      * @since 10.2
  385.      */
  386.     public FieldPVCoordinates<UnivariateDerivative1> toUnivariateDerivative1PV() {

  388.         final double   r2            = position.getNormSq();
  389.         final double   r             = FastMath.sqrt(r2);
  390.         final double   pvOr2         = Vector3D.dotProduct(position, velocity) / r2;
  391.         final double   a             = acceleration.getNorm();
  392.         final double   aOr           = a / r;
  393.         final Vector3D keplerianJerk = new Vector3D(-3 * pvOr2, acceleration, -aOr, velocity);

  395.         final UnivariateDerivative1 x0 = new UnivariateDerivative1(position.getX(),     velocity.getX());
  396.         final UnivariateDerivative1 y0 = new UnivariateDerivative1(position.getY(),     velocity.getY());
  397.         final UnivariateDerivative1 z0 = new UnivariateDerivative1(position.getZ(),     velocity.getZ());
  398.         final UnivariateDerivative1 x1 = new UnivariateDerivative1(velocity.getX(),     acceleration.getX());
  399.         final UnivariateDerivative1 y1 = new UnivariateDerivative1(velocity.getY(),     acceleration.getY());
  400.         final UnivariateDerivative1 z1 = new UnivariateDerivative1(velocity.getZ(),     acceleration.getZ());
  401.         final UnivariateDerivative1 x2 = new UnivariateDerivative1(acceleration.getX(), keplerianJerk.getX());
  402.         final UnivariateDerivative1 y2 = new UnivariateDerivative1(acceleration.getY(), keplerianJerk.getY());
  403.         final UnivariateDerivative1 z2 = new UnivariateDerivative1(acceleration.getZ(), keplerianJerk.getZ());

  405.         return new FieldPVCoordinates<>(new FieldVector3D<>(x0, y0, z0),
  406.                                         new FieldVector3D<>(x1, y1, z1),
  407.                                         new FieldVector3D<>(x2, y2, z2));

  409.     }

  411.     /** Transform the instance to a {@link FieldPVCoordinates}&lt;{@link UnivariateDerivative2}&gt;.
  412.      * <p>
  413.      * The {@link UnivariateDerivative2} coordinates correspond to time-derivatives up
  414.      * to the order 2.
  415.      * As derivation order is 2, the second derivative of velocity (which
  416.      * is also the first derivative of acceleration) will be computed as a Keplerian-only jerk,
  417.      * and the second derivative of acceleration will be computed as a Keplerian-only jounce.
  418.      * </p>
  419.      * @return pv coordinates with time-derivatives embedded within the coordinates
  420.      * @since 10.2
  421.      */
  422.     public FieldPVCoordinates<UnivariateDerivative2> toUnivariateDerivative2PV() {

  424.         final double   r2              = position.getNormSq();
  425.         final double   r               = FastMath.sqrt(r2);
  426.         final double   pvOr2           = Vector3D.dotProduct(position, velocity) / r2;
  427.         final double   a               = acceleration.getNorm();
  428.         final double   aOr             = a / r;
  429.         final Vector3D keplerianJerk   = new Vector3D(-3 * pvOr2, acceleration, -aOr, velocity);
  430.         final double   v2              = velocity.getNormSq();
  431.         final double   pa              = Vector3D.dotProduct(position, acceleration);
  432.         final double   aj              = Vector3D.dotProduct(acceleration, keplerianJerk);
  433.         final Vector3D keplerianJounce = new Vector3D(-3 * (v2 + pa) / r2 + 15 * pvOr2 * pvOr2 - aOr, acceleration,
  434.                                                       4 * aOr * pvOr2 - aj / (a * r), velocity);

  436.         final UnivariateDerivative2 x0 = new UnivariateDerivative2(position.getX(),     velocity.getX(),      acceleration.getX());
  437.         final UnivariateDerivative2 y0 = new UnivariateDerivative2(position.getY(),     velocity.getY(),      acceleration.getY());
  438.         final UnivariateDerivative2 z0 = new UnivariateDerivative2(position.getZ(),     velocity.getZ(),      acceleration.getZ());
  439.         final UnivariateDerivative2 x1 = new UnivariateDerivative2(velocity.getX(),     acceleration.getX(),  keplerianJerk.getX());
  440.         final UnivariateDerivative2 y1 = new UnivariateDerivative2(velocity.getY(),     acceleration.getY(),  keplerianJerk.getY());
  441.         final UnivariateDerivative2 z1 = new UnivariateDerivative2(velocity.getZ(),     acceleration.getZ(),  keplerianJerk.getZ());
  442.         final UnivariateDerivative2 x2 = new UnivariateDerivative2(acceleration.getX(), keplerianJerk.getX(), keplerianJounce.getX());
  443.         final UnivariateDerivative2 y2 = new UnivariateDerivative2(acceleration.getY(), keplerianJerk.getY(), keplerianJounce.getY());
  444.         final UnivariateDerivative2 z2 = new UnivariateDerivative2(acceleration.getZ(), keplerianJerk.getZ(), keplerianJounce.getZ());

  446.         return new FieldPVCoordinates<>(new FieldVector3D<>(x0, y0, z0),
  447.                                         new FieldVector3D<>(x1, y1, z1),
  448.                                         new FieldVector3D<>(x2, y2, z2));

  450.     }

  452.     /** Estimate velocity between two positions.
  453.      * <p>Estimation is based on a simple fixed velocity translation
  454.      * during the time interval between the two positions.</p>
  455.      * @param start start position
  456.      * @param end end position
  457.      * @param dt time elapsed between the dates of the two positions
  458.      * @return velocity allowing to go from start to end positions
  459.      */
  460.     public static Vector3D estimateVelocity(final Vector3D start, final Vector3D end, final double dt) {
  461.         final double scale = 1.0 / dt;
  462.         return new Vector3D(scale, end, -scale, start);
  463.     }

  465.     /** Get a time-shifted state.
  466.      * <p>
  467.      * The state can be slightly shifted to close dates. This shift is based on
  468.      * a simple Taylor expansion. It is <em>not</em> intended as a replacement for
  469.      * proper orbit propagation (it is not even Keplerian!) but should be sufficient
  470.      * for either small time shifts or coarse accuracy.
  471.      * </p>
  472.      * @param dt time shift in seconds
  473.      * @return a new state, shifted with respect to the instance (which is immutable)
  474.      */
  475.     public PVCoordinates shiftedBy(final double dt) {
  476.         return new PVCoordinates(new Vector3D(1, position, dt, velocity, 0.5 * dt * dt, acceleration),
  477.                                  new Vector3D(1, velocity, dt, acceleration),
  478.                                  acceleration);
  479.     }

  481.     /** Gets the position.
  482.      * @return the position vector (m).
  483.      */
  484.     public Vector3D getPosition() {
  485.         return position;
  486.     }

  488.     /** Gets the velocity.
  489.      * @return the velocity vector (m/s).
  490.      */
  491.     public Vector3D getVelocity() {
  492.         return velocity;
  493.     }

  495.     /** Gets the acceleration.
  496.      * @return the acceleration vector (m/s²).
  497.      */
  498.     public Vector3D getAcceleration() {
  499.         return acceleration;
  500.     }

  502.     /** Gets the momentum.
  503.      * <p>This vector is the p &otimes; v where p is position, v is velocity
  504.      * and &otimes; is cross product. To get the real physical angular momentum
  505.      * you need to multiply this vector by the mass.</p>
  506.      * <p>The returned vector is recomputed each time this method is called, it
  507.      * is not cached.</p>
  508.      * @return a new instance of the momentum vector (m²/s).
  509.      */
  510.     public Vector3D getMomentum() {
  511.         return Vector3D.crossProduct(position, velocity);
  512.     }

  514.     /**
  515.      * Get the angular velocity (spin) of this point as seen from the origin.
  516.      *
  517.      * <p> The angular velocity vector is parallel to the {@link #getMomentum()
  518.      * angular momentum} and is computed by ω = p &times; v / ||p||²
  519.      *
  520.      * @return the angular velocity vector
  521.      * @see <a href="http://en.wikipedia.org/wiki/Angular_velocity">Angular Velocity on
  522.      *      Wikipedia</a>
  523.      */
  524.     public Vector3D getAngularVelocity() {
  525.         return this.getMomentum().scalarMultiply(1.0 / this.getPosition().getNormSq());
  526.     }

  528.     /** Get the opposite of the instance.
  529.      * @return a new position-velocity which is opposite to the instance
  530.      */
  531.     public PVCoordinates negate() {
  532.         return new PVCoordinates(position.negate(), velocity.negate(), acceleration.negate());
  533.     }

  535.     /** Normalize the position part of the instance.
  536.      * <p>
  537.      * The computed coordinates first component (position) will be a
  538.      * normalized vector, the second component (velocity) will be the
  539.      * derivative of the first component (hence it will generally not
  540.      * be normalized), and the third component (acceleration) will be the
  541.      * derivative of the second component (hence it will generally not
  542.      * be normalized).
  543.      * </p>
  544.      * @return a new instance, with first component normalized and
  545.      * remaining component computed to have consistent derivatives
  546.      */
  547.     public PVCoordinates normalize() {
  548.         final double   inv     = 1.0 / position.getNorm();
  549.         final Vector3D u       = new Vector3D(inv, position);
  550.         final Vector3D v       = new Vector3D(inv, velocity);
  551.         final Vector3D w       = new Vector3D(inv, acceleration);
  552.         final double   uv      = Vector3D.dotProduct(u, v);
  553.         final double   v2      = Vector3D.dotProduct(v, v);
  554.         final double   uw      = Vector3D.dotProduct(u, w);
  555.         final Vector3D uDot    = new Vector3D(1, v, -uv, u);
  556.         final Vector3D uDotDot = new Vector3D(1, w, -2 * uv, v, 3 * uv * uv - v2 - uw, u);
  557.         return new PVCoordinates(u, uDot, uDotDot);
  558.     }

  560.     /** Compute the cross-product of two instances.
  561.      * @param pv1 first instances
  562.      * @param pv2 second instances
  563.      * @return the cross product v1 ^ v2 as a new instance
  564.      */
  565.     public static PVCoordinates crossProduct(final PVCoordinates pv1, final PVCoordinates pv2) {
  566.         final Vector3D p1 = pv1.position;
  567.         final Vector3D v1 = pv1.velocity;
  568.         final Vector3D a1 = pv1.acceleration;
  569.         final Vector3D p2 = pv2.position;
  570.         final Vector3D v2 = pv2.velocity;
  571.         final Vector3D a2 = pv2.acceleration;
  572.         return new PVCoordinates(Vector3D.crossProduct(p1, p2),
  573.                                  new Vector3D(1, Vector3D.crossProduct(p1, v2),
  574.                                               1, Vector3D.crossProduct(v1, p2)),
  575.                                  new Vector3D(1, Vector3D.crossProduct(p1, a2),
  576.                                               2, Vector3D.crossProduct(v1, v2),
  577.                                               1, Vector3D.crossProduct(a1, p2)));
  578.     }

  580.     /** Return a string representation of this position/velocity pair.
  581.      * @return string representation of this position/velocity pair
  582.      */
  583.     public String toString() {
  584.         final String comma = ", ";
  585.         return new StringBuffer().append('{').append("P(").
  586.                 append(position.getX()).append(comma).
  587.                 append(position.getY()).append(comma).
  588.                 append(position.getZ()).append("), V(").
  589.                 append(velocity.getX()).append(comma).
  590.                 append(velocity.getY()).append(comma).
  591.                 append(velocity.getZ()).append("), A(").
  592.                 append(acceleration.getX()).append(comma).
  593.                 append(acceleration.getY()).append(comma).
  594.                 append(acceleration.getZ()).append(")}").toString();
  595.     }

  597.     /** Replace the instance with a data transfer object for serialization.
  598.      * @return data transfer object that will be serialized
  599.      */
  600.     private Object writeReplace() {
  601.         return new DTO(this);
  602.     }

  604.     /** Internal class used only for serialization. */
  605.     private static class DTO implements Serializable {

  607.         /** Serializable UID. */
  608.         private static final long serialVersionUID = 20140723L;

  610.         /** Double values. */
  611.         private double[] d;

  613.         /** Simple constructor.
  614.          * @param pv instance to serialize
  615.          */
  616.         private DTO(final PVCoordinates pv) {
  617.             this.d = new double[] {
  618.                 pv.getPosition().getX(),     pv.getPosition().getY(),     pv.getPosition().getZ(),
  619.                 pv.getVelocity().getX(),     pv.getVelocity().getY(),     pv.getVelocity().getZ(),
  620.                 pv.getAcceleration().getX(), pv.getAcceleration().getY(), pv.getAcceleration().getZ(),
  621.             };
  622.         }

  624.         /** Replace the deserialized data transfer object with a {@link PVCoordinates}.
  625.          * @return replacement {@link PVCoordinates}
  626.          */
  627.         private Object readResolve() {
  628.             return new PVCoordinates(new Vector3D(d[0], d[1], d[2]),
  629.                                      new Vector3D(d[3], d[4], d[5]),
  630.                                      new Vector3D(d[6], d[7], d[8]));
  631.         }

  633.     }

  635. }
Created with JaCoCo 0.8.6.202009150832