FieldPVCoordinates.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 org.hipparchus.Field;
  20. import org.hipparchus.RealFieldElement;
  21. import org.hipparchus.analysis.differentiation.FDSFactory;
  22. import org.hipparchus.analysis.differentiation.FieldDerivativeStructure;
  23. import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative1;
  24. import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative2;
  25. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  26. import org.hipparchus.util.FastMath;
  27. import org.orekit.errors.OrekitException;
  28. import org.orekit.errors.OrekitMessages;
  29. import org.orekit.time.TimeShiftable;

  31. /** Simple container for Position/Velocity pairs, using {@link RealFieldElement}.
  32.  * <p>
  33.  * The state can be slightly shifted to close dates. This shift is based on
  34.  * a simple linear model. It is <em>not</em> intended as a replacement for
  35.  * proper orbit propagation (it is not even Keplerian!) but should be sufficient
  36.  * for either small time shifts or coarse accuracy.
  37.  * </p>
  38.  * <p>
  39.  * This class is the angular counterpart to {@link FieldAngularCoordinates}.
  40.  * </p>
  41.  * <p>Instances of this class are guaranteed to be immutable.</p>
  42.  * @param <T> the type of the field elements
  43.  * @author Luc Maisonobe
  44.  * @since 6.0
  45.  * @see PVCoordinates
  46.  */
  47. public class FieldPVCoordinates<T extends RealFieldElement<T>>
  48.     implements TimeShiftable<FieldPVCoordinates<T>> {

  50.     /** The position. */
  51.     private final FieldVector3D<T> position;

  53.     /** The velocity. */
  54.     private final FieldVector3D<T> velocity;

  56.     /** The acceleration. */
  57.     private final FieldVector3D<T> acceleration;

  59.     /** Builds a FieldPVCoordinates triplet with zero acceleration.
  60.      * @param position the position vector (m)
  61.      * @param velocity the velocity vector (m/s)
  62.      */
  63.     public FieldPVCoordinates(final FieldVector3D<T> position, final FieldVector3D<T> velocity) {
  64.         this.position     = position;
  65.         this.velocity     = velocity;
  66.         final T zero      = position.getX().getField().getZero();
  67.         this.acceleration = new FieldVector3D<>(zero, zero, zero);
  68.     }

  70.     /** Builds a FieldPVCoordinates triplet.
  71.      * @param position the position vector (m)
  72.      * @param velocity the velocity vector (m/s)
  73.      * @param acceleration the acceleration vector (m/s²)
  74.      */
  75.     public FieldPVCoordinates(final FieldVector3D<T> position, final FieldVector3D<T> velocity,
  76.                               final FieldVector3D<T> acceleration) {
  77.         this.position     = position;
  78.         this.velocity     = velocity;
  79.         this.acceleration = acceleration;
  80.     }

  82.     /** Builds a FieldPVCoordinates from a field and a regular PVCoordinates.
  83.      * @param field field for the components
  84.      * @param pv PVCoordinates triplet to convert
  85.      */
  86.     public FieldPVCoordinates(final Field<T> field, final PVCoordinates pv) {
  87.         this.position     = new FieldVector3D<>(field, pv.getPosition());
  88.         this.velocity     = new FieldVector3D<>(field, pv.getVelocity());
  89.         this.acceleration = new FieldVector3D<>(field, pv.getAcceleration());
  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 FieldPVCoordinates(final double a, final FieldPVCoordinates<T> pv) {
  99.         position     = new FieldVector3D<>(a, pv.position);
  100.         velocity     = new FieldVector3D<>(a, pv.velocity);
  101.         acceleration = new FieldVector3D<>(a, pv.acceleration);
  102.     }

  104.     /** Multiplicative constructor.
  105.      * <p>Build a PVCoordinates from another one and a scale factor.</p>
  106.      * <p>The PVCoordinates built will be a * pv</p>
  107.      * @param a scale factor
  108.      * @param pv base (unscaled) PVCoordinates
  109.      */
  110.     public FieldPVCoordinates(final T a, final FieldPVCoordinates<T> pv) {
  111.         position     = new FieldVector3D<>(a, pv.position);
  112.         velocity     = new FieldVector3D<>(a, pv.velocity);
  113.         acceleration = new FieldVector3D<>(a, pv.acceleration);
  114.     }

  116.     /** Multiplicative constructor.
  117.      * <p>Build a PVCoordinates from another one and a scale factor.</p>
  118.      * <p>The PVCoordinates built will be a * pv</p>
  119.      * @param a scale factor
  120.      * @param pv base (unscaled) PVCoordinates
  121.      */
  122.     public FieldPVCoordinates(final T a, final PVCoordinates pv) {
  123.         position     = new FieldVector3D<>(a, pv.getPosition());
  124.         velocity     = new FieldVector3D<>(a, pv.getVelocity());
  125.         acceleration = new FieldVector3D<>(a, pv.getAcceleration());
  126.     }

  128.     /** Subtractive constructor.
  129.      * <p>Build a relative PVCoordinates from a start and an end position.</p>
  130.      * <p>The PVCoordinates built will be end - start.</p>
  131.      * @param start Starting PVCoordinates
  132.      * @param end ending PVCoordinates
  133.      */
  134.     public FieldPVCoordinates(final FieldPVCoordinates<T> start, final FieldPVCoordinates<T> end) {
  135.         this.position     = end.position.subtract(start.position);
  136.         this.velocity     = end.velocity.subtract(start.velocity);
  137.         this.acceleration = end.acceleration.subtract(start.acceleration);
  138.     }

  140.     /** Linear constructor.
  141.      * <p>Build a PVCoordinates from two other ones and corresponding scale factors.</p>
  142.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2</p>
  143.      * @param a1 first scale factor
  144.      * @param pv1 first base (unscaled) PVCoordinates
  145.      * @param a2 second scale factor
  146.      * @param pv2 second base (unscaled) PVCoordinates
  147.      */
  148.     public FieldPVCoordinates(final double a1, final FieldPVCoordinates<T> pv1,
  149.                               final double a2, final FieldPVCoordinates<T> pv2) {
  150.         position     = new FieldVector3D<>(a1, pv1.position, a2, pv2.position);
  151.         velocity     = new FieldVector3D<>(a1, pv1.velocity, a2, pv2.velocity);
  152.         acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration);
  153.     }

  155.     /** Linear constructor.
  156.      * <p>Build a PVCoordinates from two other ones and corresponding scale factors.</p>
  157.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2</p>
  158.      * @param a1 first scale factor
  159.      * @param pv1 first base (unscaled) PVCoordinates
  160.      * @param a2 second scale factor
  161.      * @param pv2 second base (unscaled) PVCoordinates
  162.      */
  163.     public FieldPVCoordinates(final T a1, final FieldPVCoordinates<T> pv1,
  164.                               final T a2, final FieldPVCoordinates<T> pv2) {
  165.         position     = new FieldVector3D<>(a1, pv1.position, a2, pv2.position);
  166.         velocity     = new FieldVector3D<>(a1, pv1.velocity, a2, pv2.velocity);
  167.         acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration);
  168.     }

  170.     /** Linear constructor.
  171.      * <p>Build a PVCoordinates from two other ones and corresponding scale factors.</p>
  172.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2</p>
  173.      * @param a1 first scale factor
  174.      * @param pv1 first base (unscaled) PVCoordinates
  175.      * @param a2 second scale factor
  176.      * @param pv2 second base (unscaled) PVCoordinates
  177.      */
  178.     public FieldPVCoordinates(final T a1, final PVCoordinates pv1,
  179.                               final T a2, final PVCoordinates pv2) {
  180.         position     = new FieldVector3D<>(a1, pv1.getPosition(), a2, pv2.getPosition());
  181.         velocity     = new FieldVector3D<>(a1, pv1.getVelocity(), a2, pv2.getVelocity());
  182.         acceleration = new FieldVector3D<>(a1, pv1.getAcceleration(), a2, pv2.getAcceleration());
  183.     }

  185.     /** Linear constructor.
  186.      * <p>Build a PVCoordinates from three other ones and corresponding scale factors.</p>
  187.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3</p>
  188.      * @param a1 first scale factor
  189.      * @param pv1 first base (unscaled) PVCoordinates
  190.      * @param a2 second scale factor
  191.      * @param pv2 second base (unscaled) PVCoordinates
  192.      * @param a3 third scale factor
  193.      * @param pv3 third base (unscaled) PVCoordinates
  194.      */
  195.     public FieldPVCoordinates(final double a1, final FieldPVCoordinates<T> pv1,
  196.                               final double a2, final FieldPVCoordinates<T> pv2,
  197.                               final double a3, final FieldPVCoordinates<T> pv3) {
  198.         position     = new FieldVector3D<>(a1, pv1.position,     a2, pv2.position,     a3, pv3.position);
  199.         velocity     = new FieldVector3D<>(a1, pv1.velocity,     a2, pv2.velocity,     a3, pv3.velocity);
  200.         acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration, a3, pv3.acceleration);
  201.     }

  203.     /** Linear constructor.
  204.      * <p>Build a PVCoordinates from three other ones and corresponding scale factors.</p>
  205.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3</p>
  206.      * @param a1 first scale factor
  207.      * @param pv1 first base (unscaled) PVCoordinates
  208.      * @param a2 second scale factor
  209.      * @param pv2 second base (unscaled) PVCoordinates
  210.      * @param a3 third scale factor
  211.      * @param pv3 third base (unscaled) PVCoordinates
  212.      */
  213.     public FieldPVCoordinates(final T a1, final FieldPVCoordinates<T> pv1,
  214.                               final T a2, final FieldPVCoordinates<T> pv2,
  215.                               final T a3, final FieldPVCoordinates<T> pv3) {
  216.         position     = new FieldVector3D<>(a1, pv1.position,     a2, pv2.position,     a3, pv3.position);
  217.         velocity     = new FieldVector3D<>(a1, pv1.velocity,     a2, pv2.velocity,     a3, pv3.velocity);
  218.         acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration, a3, pv3.acceleration);
  219.     }

  221.     /** Linear constructor.
  222.      * <p>Build a PVCoordinates from three other ones and corresponding scale factors.</p>
  223.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3</p>
  224.      * @param a1 first scale factor
  225.      * @param pv1 first base (unscaled) PVCoordinates
  226.      * @param a2 second scale factor
  227.      * @param pv2 second base (unscaled) PVCoordinates
  228.      * @param a3 third scale factor
  229.      * @param pv3 third base (unscaled) PVCoordinates
  230.      */
  231.     public FieldPVCoordinates(final T a1, final PVCoordinates pv1,
  232.                               final T a2, final PVCoordinates pv2,
  233.                               final T a3, final PVCoordinates pv3) {
  234.         position     = new FieldVector3D<>(a1, pv1.getPosition(),     a2, pv2.getPosition(),     a3, pv3.getPosition());
  235.         velocity     = new FieldVector3D<>(a1, pv1.getVelocity(),     a2, pv2.getVelocity(),     a3, pv3.getVelocity());
  236.         acceleration = new FieldVector3D<>(a1, pv1.getAcceleration(), a2, pv2.getAcceleration(), a3, pv3.getAcceleration());
  237.     }

  239.     /** Linear constructor.
  240.      * <p>Build a PVCoordinates from four other ones and corresponding scale factors.</p>
  241.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4</p>
  242.      * @param a1 first scale factor
  243.      * @param pv1 first base (unscaled) PVCoordinates
  244.      * @param a2 second scale factor
  245.      * @param pv2 second base (unscaled) PVCoordinates
  246.      * @param a3 third scale factor
  247.      * @param pv3 third base (unscaled) PVCoordinates
  248.      * @param a4 fourth scale factor
  249.      * @param pv4 fourth base (unscaled) PVCoordinates
  250.      */
  251.     public FieldPVCoordinates(final double a1, final FieldPVCoordinates<T> pv1,
  252.                               final double a2, final FieldPVCoordinates<T> pv2,
  253.                               final double a3, final FieldPVCoordinates<T> pv3,
  254.                               final double a4, final FieldPVCoordinates<T> pv4) {
  255.         position     = new FieldVector3D<>(a1, pv1.position,     a2, pv2.position,     a3, pv3.position,     a4, pv4.position);
  256.         velocity     = new FieldVector3D<>(a1, pv1.velocity,     a2, pv2.velocity,     a3, pv3.velocity,     a4, pv4.velocity);
  257.         acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration, a3, pv3.acceleration, a4, pv4.acceleration);
  258.     }

  260.     /** Linear constructor.
  261.      * <p>Build a PVCoordinates from four other ones and corresponding scale factors.</p>
  262.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4</p>
  263.      * @param a1 first scale factor
  264.      * @param pv1 first base (unscaled) PVCoordinates
  265.      * @param a2 second scale factor
  266.      * @param pv2 second base (unscaled) PVCoordinates
  267.      * @param a3 third scale factor
  268.      * @param pv3 third base (unscaled) PVCoordinates
  269.      * @param a4 fourth scale factor
  270.      * @param pv4 fourth base (unscaled) PVCoordinates
  271.      */
  272.     public FieldPVCoordinates(final T a1, final FieldPVCoordinates<T> pv1,
  273.                               final T a2, final FieldPVCoordinates<T> pv2,
  274.                               final T a3, final FieldPVCoordinates<T> pv3,
  275.                               final T a4, final FieldPVCoordinates<T> pv4) {
  276.         position     = new FieldVector3D<>(a1, pv1.position,     a2, pv2.position,     a3, pv3.position,     a4, pv4.position);
  277.         velocity     = new FieldVector3D<>(a1, pv1.velocity,     a2, pv2.velocity,     a3, pv3.velocity,     a4, pv4.velocity);
  278.         acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration, a3, pv3.acceleration, a4, pv4.acceleration);
  279.     }

  281.     /** Linear constructor.
  282.      * <p>Build a PVCoordinates from four other ones and corresponding scale factors.</p>
  283.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4</p>
  284.      * @param a1 first scale factor
  285.      * @param pv1 first base (unscaled) PVCoordinates
  286.      * @param a2 second scale factor
  287.      * @param pv2 second base (unscaled) PVCoordinates
  288.      * @param a3 third scale factor
  289.      * @param pv3 third base (unscaled) PVCoordinates
  290.      * @param a4 fourth scale factor
  291.      * @param pv4 fourth base (unscaled) PVCoordinates
  292.      */
  293.     public FieldPVCoordinates(final T a1, final PVCoordinates pv1,
  294.                               final T a2, final PVCoordinates pv2,
  295.                               final T a3, final PVCoordinates pv3,
  296.                               final T a4, final PVCoordinates pv4) {
  297.         position     = new FieldVector3D<>(a1, pv1.getPosition(),     a2, pv2.getPosition(),
  298.                                            a3, pv3.getPosition(),     a4, pv4.getPosition());
  299.         velocity     = new FieldVector3D<>(a1, pv1.getVelocity(),     a2, pv2.getVelocity(),
  300.                                            a3, pv3.getVelocity(),     a4, pv4.getVelocity());
  301.         acceleration = new FieldVector3D<>(a1, pv1.getAcceleration(), a2, pv2.getAcceleration(),
  302.                                            a3, pv3.getAcceleration(), a4, pv4.getAcceleration());
  303.     }

  305.     /** Builds a FieldPVCoordinates triplet from  a {@link FieldVector3D}&lt;{@link FieldDerivativeStructure}&gt;.
  306.      * <p>
  307.      * The vector components must have time as their only derivation parameter and
  308.      * have consistent derivation orders.
  309.      * </p>
  310.      * @param p vector with time-derivatives embedded within the coordinates
  311.      * @since 9.2
  312.      */
  313.     public FieldPVCoordinates(final FieldVector3D<FieldDerivativeStructure<T>> p) {
  314.         position = new FieldVector3D<>(p.getX().getValue(), p.getY().getValue(), p.getZ().getValue());
  315.         if (p.getX().getOrder() >= 1) {
  316.             velocity = new FieldVector3D<>(p.getX().getPartialDerivative(1),
  317.                                            p.getY().getPartialDerivative(1),
  318.                                            p.getZ().getPartialDerivative(1));
  319.             if (p.getX().getOrder() >= 2) {
  320.                 acceleration = new FieldVector3D<>(p.getX().getPartialDerivative(2),
  321.                                                    p.getY().getPartialDerivative(2),
  322.                                                    p.getZ().getPartialDerivative(2));
  323.             } else {
  324.                 acceleration = FieldVector3D.getZero(position.getX().getField());
  325.             }
  326.         } else {
  327.             final FieldVector3D<T> zero = FieldVector3D.getZero(position.getX().getField());
  328.             velocity     = zero;
  329.             acceleration = zero;
  330.         }
  331.     }

  333.     /** Get fixed position/velocity at origin (both p, v and a are zero vectors).
  334.      * @param field field for the components
  335.      * @param <T> the type of the field elements
  336.      * @return a new fixed position/velocity at origin
  337.      */
  338.     public static <T extends RealFieldElement<T>> FieldPVCoordinates<T> getZero(final Field<T> field) {
  339.         return new FieldPVCoordinates<>(field, PVCoordinates.ZERO);
  340.     }

  342.     /** Transform the instance to a {@link FieldVector3D}&lt;{@link FieldDerivativeStructure}&gt;.
  343.      * <p>
  344.      * The {@link FieldDerivativeStructure} coordinates correspond to time-derivatives up
  345.      * to the user-specified order.
  346.      * </p>
  347.      * @param order derivation order for the vector components (must be either 0, 1 or 2)
  348.      * @return vector with time-derivatives embedded within the coordinates
  349.           * @since 9.2
  350.      */
  351.     public FieldVector3D<FieldDerivativeStructure<T>> toDerivativeStructureVector(final int order) {

  353.         final FDSFactory<T> factory;
  354.         final FieldDerivativeStructure<T> x;
  355.         final FieldDerivativeStructure<T> y;
  356.         final FieldDerivativeStructure<T> z;
  357.         switch(order) {
  358.             case 0 :
  359.                 factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
  360.                 x = factory.build(position.getX());
  361.                 y = factory.build(position.getY());
  362.                 z = factory.build(position.getZ());
  363.                 break;
  364.             case 1 :
  365.                 factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
  366.                 x = factory.build(position.getX(), velocity.getX());
  367.                 y = factory.build(position.getY(), velocity.getY());
  368.                 z = factory.build(position.getZ(), velocity.getZ());
  369.                 break;
  370.             case 2 :
  371.                 factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
  372.                 x = factory.build(position.getX(), velocity.getX(), acceleration.getX());
  373.                 y = factory.build(position.getY(), velocity.getY(), acceleration.getY());
  374.                 z = factory.build(position.getZ(), velocity.getZ(), acceleration.getZ());
  375.                 break;
  376.             default :
  377.                 throw new OrekitException(OrekitMessages.OUT_OF_RANGE_DERIVATION_ORDER, order);
  378.         }

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

  382.     }

  384.     /** Transform the instance to a {@link FieldVector3D}&lt;{@link FieldUnivariateDerivative1}&gt;.
  385.      * <p>
  386.      * The {@link FieldUnivariateDerivative1} coordinates correspond to time-derivatives up
  387.      * to the order 1.
  388.      * </p>
  389.      * @return vector with time-derivatives embedded within the coordinates
  390.      * @see #toUnivariateDerivative2Vector()
  391.      * @since 10.2
  392.      */
  393.     public FieldVector3D<FieldUnivariateDerivative1<T>> toUnivariateDerivative1Vector() {

  395.         final FieldUnivariateDerivative1<T> x = new FieldUnivariateDerivative1<>(position.getX(), velocity.getX());
  396.         final FieldUnivariateDerivative1<T> y = new FieldUnivariateDerivative1<>(position.getY(), velocity.getY());
  397.         final FieldUnivariateDerivative1<T> z = new FieldUnivariateDerivative1<>(position.getZ(), velocity.getZ());

  399.         return new FieldVector3D<>(x, y, z);
  400.     }

  402.     /** Transform the instance to a {@link FieldVector3D}&lt;{@link FieldUnivariateDerivative2}&gt;.
  403.      * <p>
  404.      * The {@link FieldUnivariateDerivative2} coordinates correspond to time-derivatives up
  405.      * to the order 2.
  406.      * </p>
  407.      * @return vector with time-derivatives embedded within the coordinates
  408.      * @see #toUnivariateDerivative1Vector()
  409.      * @since 10.2
  410.      */
  411.     public FieldVector3D<FieldUnivariateDerivative2<T>> toUnivariateDerivative2Vector() {

  413.         final FieldUnivariateDerivative2<T> x = new FieldUnivariateDerivative2<>(position.getX(), velocity.getX(), acceleration.getX());
  414.         final FieldUnivariateDerivative2<T> y = new FieldUnivariateDerivative2<>(position.getY(), velocity.getY(), acceleration.getY());
  415.         final FieldUnivariateDerivative2<T> z = new FieldUnivariateDerivative2<>(position.getZ(), velocity.getZ(), acceleration.getZ());

  417.         return new FieldVector3D<>(x, y, z);
  418.     }

  420.     /** Transform the instance to a {@link FieldPVCoordinates}&lt;{@link FieldDerivativeStructure}&gt;.
  421.      * <p>
  422.      * The {@link FieldDerivativeStructure} coordinates correspond to time-derivatives up
  423.      * to the user-specified order. As both the instance components {@link #getPosition() position},
  424.      * {@link #getVelocity() velocity} and {@link #getAcceleration() acceleration} and the
  425.      * {@link FieldDerivativeStructure#getPartialDerivative(int...) derivatives} of the components
  426.      * holds time-derivatives, there are several ways to retrieve these derivatives. If for example
  427.      * the {@code order} is set to 2, then both {@code pv.getPosition().getX().getPartialDerivative(2)},
  428.      * {@code pv.getVelocity().getX().getPartialDerivative(1)} and
  429.      * {@code pv.getAcceleration().getX().getValue()} return the exact same value.
  430.      * </p>
  431.      * <p>
  432.      * If derivation order is 1, the first derivative of acceleration will be computed as a
  433.      * Keplerian-only jerk. If derivation order is 2, the second derivative of velocity (which
  434.      * is also the first derivative of acceleration) will be computed as a Keplerian-only jerk,
  435.      * and the second derivative of acceleration will be computed as a Keplerian-only jounce.
  436.      * </p>
  437.      * @param order derivation order for the vector components (must be either 0, 1 or 2)
  438.      * @return pv coordinates with time-derivatives embedded within the coordinates
  439.           * @since 9.2
  440.      */
  441.     public FieldPVCoordinates<FieldDerivativeStructure<T>> toDerivativeStructurePV(final int order) {

  443.         final FDSFactory<T> factory;
  444.         final FieldDerivativeStructure<T> x0;
  445.         final FieldDerivativeStructure<T> y0;
  446.         final FieldDerivativeStructure<T> z0;
  447.         final FieldDerivativeStructure<T> x1;
  448.         final FieldDerivativeStructure<T> y1;
  449.         final FieldDerivativeStructure<T> z1;
  450.         final FieldDerivativeStructure<T> x2;
  451.         final FieldDerivativeStructure<T> y2;
  452.         final FieldDerivativeStructure<T> z2;
  453.         switch(order) {
  454.             case 0 :
  455.                 factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
  456.                 x0 = factory.build(position.getX());
  457.                 y0 = factory.build(position.getY());
  458.                 z0 = factory.build(position.getZ());
  459.                 x1 = factory.build(velocity.getX());
  460.                 y1 = factory.build(velocity.getY());
  461.                 z1 = factory.build(velocity.getZ());
  462.                 x2 = factory.build(acceleration.getX());
  463.                 y2 = factory.build(acceleration.getY());
  464.                 z2 = factory.build(acceleration.getZ());
  465.                 break;
  466.             case 1 : {
  467.                 factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
  468.                 final T                r2            = position.getNormSq();
  469.                 final T                r             = r2.sqrt();
  470.                 final T                pvOr2         = FieldVector3D.dotProduct(position, velocity).divide(r2);
  471.                 final T                a             = acceleration.getNorm();
  472.                 final T                aOr           = a.divide(r);
  473.                 final FieldVector3D<T> keplerianJerk = new FieldVector3D<>(pvOr2.multiply(-3), acceleration,
  474.                                                                            aOr.negate(), velocity);
  475.                 x0 = factory.build(position.getX(),     velocity.getX());
  476.                 y0 = factory.build(position.getY(),     velocity.getY());
  477.                 z0 = factory.build(position.getZ(),     velocity.getZ());
  478.                 x1 = factory.build(velocity.getX(),     acceleration.getX());
  479.                 y1 = factory.build(velocity.getY(),     acceleration.getY());
  480.                 z1 = factory.build(velocity.getZ(),     acceleration.getZ());
  481.                 x2 = factory.build(acceleration.getX(), keplerianJerk.getX());
  482.                 y2 = factory.build(acceleration.getY(), keplerianJerk.getY());
  483.                 z2 = factory.build(acceleration.getZ(), keplerianJerk.getZ());
  484.                 break;
  485.             }
  486.             case 2 : {
  487.                 factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
  488.                 final T                r2              = position.getNormSq();
  489.                 final T                r               = r2.sqrt();
  490.                 final T                pvOr2           = FieldVector3D.dotProduct(position, velocity).divide(r2);
  491.                 final T                a               = acceleration.getNorm();
  492.                 final T                aOr             = a.divide(r);
  493.                 final FieldVector3D<T> keplerianJerk   = new FieldVector3D<>(pvOr2.multiply(-3), acceleration,
  494.                                                                              aOr.negate(), velocity);
  495.                 final T                v2              = velocity.getNormSq();
  496.                 final T                pa              = FieldVector3D.dotProduct(position, acceleration);
  497.                 final T                aj              = FieldVector3D.dotProduct(acceleration, keplerianJerk);
  498.                 final FieldVector3D<T> keplerianJounce = new FieldVector3D<>(v2.add(pa).multiply(-3).divide(r2).add(pvOr2.multiply(pvOr2).multiply(15)).subtract(aOr), acceleration,
  499.                                                                              aOr.multiply(4).multiply(pvOr2).subtract(aj.divide(a.multiply(r))), velocity);
  500.                 x0 = factory.build(position.getX(),     velocity.getX(),      acceleration.getX());
  501.                 y0 = factory.build(position.getY(),     velocity.getY(),      acceleration.getY());
  502.                 z0 = factory.build(position.getZ(),     velocity.getZ(),      acceleration.getZ());
  503.                 x1 = factory.build(velocity.getX(),     acceleration.getX(),  keplerianJerk.getX());
  504.                 y1 = factory.build(velocity.getY(),     acceleration.getY(),  keplerianJerk.getY());
  505.                 z1 = factory.build(velocity.getZ(),     acceleration.getZ(),  keplerianJerk.getZ());
  506.                 x2 = factory.build(acceleration.getX(), keplerianJerk.getX(), keplerianJounce.getX());
  507.                 y2 = factory.build(acceleration.getY(), keplerianJerk.getY(), keplerianJounce.getY());
  508.                 z2 = factory.build(acceleration.getZ(), keplerianJerk.getZ(), keplerianJounce.getZ());
  509.                 break;
  510.             }
  511.             default :
  512.                 throw new OrekitException(OrekitMessages.OUT_OF_RANGE_DERIVATION_ORDER, order);
  513.         }

  515.         return new FieldPVCoordinates<>(new FieldVector3D<>(x0, y0, z0),
  516.                                         new FieldVector3D<>(x1, y1, z1),
  517.                                         new FieldVector3D<>(x2, y2, z2));

  519.     }


  522.     /** Transform the instance to a {@link FieldPVCoordinates}&lt;{@link FieldUnivariateDerivative1}&gt;.
  523.      * <p>
  524.      * The {@link FieldUnivariateDerivative1} coordinates correspond to time-derivatives up
  525.      * to the order 1.
  526.      * The first derivative of acceleration will be computed as a Keplerian-only jerk.
  527.      * </p>
  528.      * @return pv coordinates with time-derivatives embedded within the coordinates
  529.      * @since 10.2
  530.      */
  531.     public FieldPVCoordinates<FieldUnivariateDerivative1<T>> toUnivariateDerivative1PV() {

  533.         final T   r2            = position.getNormSq();
  534.         final T   r             = FastMath.sqrt(r2);
  535.         final T   pvOr2         = FieldVector3D.dotProduct(position, velocity).divide(r2);
  536.         final T   a             = acceleration.getNorm();
  537.         final T   aOr           = a.divide(r);
  538.         final FieldVector3D<T> keplerianJerk   = new FieldVector3D<>(pvOr2.multiply(-3), acceleration,
  539.                                                                      aOr.negate(), velocity);

  541.         final FieldUnivariateDerivative1<T> x0 = new FieldUnivariateDerivative1<>(position.getX(),     velocity.getX());
  542.         final FieldUnivariateDerivative1<T> y0 = new FieldUnivariateDerivative1<>(position.getY(),     velocity.getY());
  543.         final FieldUnivariateDerivative1<T> z0 = new FieldUnivariateDerivative1<>(position.getZ(),     velocity.getZ());
  544.         final FieldUnivariateDerivative1<T> x1 = new FieldUnivariateDerivative1<>(velocity.getX(),     acceleration.getX());
  545.         final FieldUnivariateDerivative1<T> y1 = new FieldUnivariateDerivative1<>(velocity.getY(),     acceleration.getY());
  546.         final FieldUnivariateDerivative1<T> z1 = new FieldUnivariateDerivative1<>(velocity.getZ(),     acceleration.getZ());
  547.         final FieldUnivariateDerivative1<T> x2 = new FieldUnivariateDerivative1<>(acceleration.getX(), keplerianJerk.getX());
  548.         final FieldUnivariateDerivative1<T> y2 = new FieldUnivariateDerivative1<>(acceleration.getY(), keplerianJerk.getY());
  549.         final FieldUnivariateDerivative1<T> z2 = new FieldUnivariateDerivative1<>(acceleration.getZ(), keplerianJerk.getZ());

  551.         return new FieldPVCoordinates<>(new FieldVector3D<>(x0, y0, z0),
  552.                                         new FieldVector3D<>(x1, y1, z1),
  553.                                         new FieldVector3D<>(x2, y2, z2));

  555.     }

  557.     /** Transform the instance to a {@link FieldPVCoordinates}&lt;{@link FieldUnivariateDerivative2}&gt;.
  558.      * <p>
  559.      * The {@link FieldUnivariateDerivative2} coordinates correspond to time-derivatives up
  560.      * to the order 2.
  561.      * As derivation order is 2, the second derivative of velocity (which
  562.      * is also the first derivative of acceleration) will be computed as a Keplerian-only jerk,
  563.      * and the second derivative of acceleration will be computed as a Keplerian-only jounce.
  564.      * </p>
  565.      * @return pv coordinates with time-derivatives embedded within the coordinates
  566.      * @since 10.2
  567.      */
  568.     public FieldPVCoordinates<FieldUnivariateDerivative2<T>> toUnivariateDerivative2PV() {

  570.         final T                r2              = position.getNormSq();
  571.         final T                r               = r2.sqrt();
  572.         final T                pvOr2           = FieldVector3D.dotProduct(position, velocity).divide(r2);
  573.         final T                a               = acceleration.getNorm();
  574.         final T                aOr             = a.divide(r);
  575.         final FieldVector3D<T> keplerianJerk   = new FieldVector3D<>(pvOr2.multiply(-3), acceleration,
  576.                                                                      aOr.negate(), velocity);
  577.         final T                v2              = velocity.getNormSq();
  578.         final T                pa              = FieldVector3D.dotProduct(position, acceleration);
  579.         final T                aj              = FieldVector3D.dotProduct(acceleration, keplerianJerk);
  580.         final FieldVector3D<T> keplerianJounce = new FieldVector3D<>(v2.add(pa).multiply(-3).divide(r2).add(pvOr2.multiply(pvOr2).multiply(15)).subtract(aOr), acceleration,
  581.                                                                      aOr.multiply(4).multiply(pvOr2).subtract(aj.divide(a.multiply(r))), velocity);

  583.         final FieldUnivariateDerivative2<T> x0 = new FieldUnivariateDerivative2<>(position.getX(),     velocity.getX(),      acceleration.getX());
  584.         final FieldUnivariateDerivative2<T> y0 = new FieldUnivariateDerivative2<>(position.getY(),     velocity.getY(),      acceleration.getY());
  585.         final FieldUnivariateDerivative2<T> z0 = new FieldUnivariateDerivative2<>(position.getZ(),     velocity.getZ(),      acceleration.getZ());
  586.         final FieldUnivariateDerivative2<T> x1 = new FieldUnivariateDerivative2<>(velocity.getX(),     acceleration.getX(),  keplerianJerk.getX());
  587.         final FieldUnivariateDerivative2<T> y1 = new FieldUnivariateDerivative2<>(velocity.getY(),     acceleration.getY(),  keplerianJerk.getY());
  588.         final FieldUnivariateDerivative2<T> z1 = new FieldUnivariateDerivative2<>(velocity.getZ(),     acceleration.getZ(),  keplerianJerk.getZ());
  589.         final FieldUnivariateDerivative2<T> x2 = new FieldUnivariateDerivative2<>(acceleration.getX(), keplerianJerk.getX(), keplerianJounce.getX());
  590.         final FieldUnivariateDerivative2<T> y2 = new FieldUnivariateDerivative2<>(acceleration.getY(), keplerianJerk.getY(), keplerianJounce.getY());
  591.         final FieldUnivariateDerivative2<T> z2 = new FieldUnivariateDerivative2<>(acceleration.getZ(), keplerianJerk.getZ(), keplerianJounce.getZ());

  593.         return new FieldPVCoordinates<>(new FieldVector3D<>(x0, y0, z0),
  594.                                         new FieldVector3D<>(x1, y1, z1),
  595.                                         new FieldVector3D<>(x2, y2, z2));

  597.     }

  599.     /** Estimate velocity between two positions.
  600.      * <p>Estimation is based on a simple fixed velocity translation
  601.      * during the time interval between the two positions.</p>
  602.      * @param start start position
  603.      * @param end end position
  604.      * @param dt time elapsed between the dates of the two positions
  605.      * @param <T> the type of the field elements
  606.      * @return velocity allowing to go from start to end positions
  607.      */
  608.     public static <T extends RealFieldElement<T>> FieldVector3D<T> estimateVelocity(final FieldVector3D<T> start,
  609.                                                                                     final FieldVector3D<T> end,
  610.                                                                                     final double dt) {
  611.         final double scale = 1.0 / dt;
  612.         return new FieldVector3D<>(scale, end, -scale, start);
  613.     }

  615.     /** Get a time-shifted state.
  616.      * <p>
  617.      * The state can be slightly shifted to close dates. This shift is based on
  618.      * a simple quadratic model. It is <em>not</em> intended as a replacement for
  619.      * proper orbit propagation (it is not even Keplerian!) but should be sufficient
  620.      * for either small time shifts or coarse accuracy.
  621.      * </p>
  622.      * @param dt time shift in seconds
  623.      * @return a new state, shifted with respect to the instance (which is immutable)
  624.      */
  625.     public FieldPVCoordinates<T> shiftedBy(final double dt) {
  626.         return new FieldPVCoordinates<>(new FieldVector3D<>(1, position, dt, velocity, 0.5 * dt * dt, acceleration),
  627.                                         new FieldVector3D<>(1, velocity, dt, acceleration),
  628.                                         acceleration);
  629.     }

  631.     /** Get a time-shifted state.
  632.      * <p>
  633.      * The state can be slightly shifted to close dates. This shift is based on
  634.      * a simple quadratic model. It is <em>not</em> intended as a replacement for
  635.      * proper orbit propagation (it is not even Keplerian!) but should be sufficient
  636.      * for either small time shifts or coarse accuracy.
  637.      * </p>
  638.      * @param dt time shift in seconds
  639.      * @return a new state, shifted with respect to the instance (which is immutable)
  640.      */
  641.     public FieldPVCoordinates<T> shiftedBy(final T dt) {
  642.         final T one = dt.getField().getOne();
  643.         return new FieldPVCoordinates<>(new FieldVector3D<>(one, position,
  644.                                                             dt, velocity,
  645.                                                             dt.multiply(dt).multiply(0.5), acceleration),
  646.                                         new FieldVector3D<>(one, velocity,
  647.                                                             dt, acceleration),
  648.                                         acceleration);
  649.     }

  651.     /** Gets the position.
  652.      * @return the position vector (m).
  653.      */
  654.     public FieldVector3D<T> getPosition() {
  655.         return position;
  656.     }

  658.     /** Gets the velocity.
  659.      * @return the velocity vector (m/s).
  660.      */
  661.     public FieldVector3D<T> getVelocity() {
  662.         return velocity;
  663.     }

  665.     /** Gets the acceleration.
  666.      * @return the acceleration vector (m/s²).
  667.      */
  668.     public FieldVector3D<T> getAcceleration() {
  669.         return acceleration;
  670.     }

  672.     /** Gets the momentum.
  673.      * <p>This vector is the p &otimes; v where p is position, v is velocity
  674.      * and &otimes; is cross product. To get the real physical angular momentum
  675.      * you need to multiply this vector by the mass.</p>
  676.      * <p>The returned vector is recomputed each time this method is called, it
  677.      * is not cached.</p>
  678.      * @return a new instance of the momentum vector (m²/s).
  679.      */
  680.     public FieldVector3D<T> getMomentum() {
  681.         return FieldVector3D.crossProduct(position, velocity);
  682.     }

  684.     /**
  685.      * Get the angular velocity (spin) of this point as seen from the origin.
  686.      *
  687.      * <p> The angular velocity vector is parallel to the {@link #getMomentum()
  688.      * angular * momentum} and is computed by ω = p &times; v / ||p||²
  689.      *
  690.      * @return the angular velocity vector
  691.      * @see <a href="http://en.wikipedia.org/wiki/Angular_velocity">Angular Velocity on
  692.      *      Wikipedia</a>
  693.      */
  694.     public FieldVector3D<T> getAngularVelocity() {
  695.         return this.getMomentum().scalarMultiply(
  696.                 this.getPosition().getNormSq().reciprocal());
  697.     }

  699.     /** Get the opposite of the instance.
  700.      * @return a new position-velocity which is opposite to the instance
  701.      */
  702.     public FieldPVCoordinates<T> negate() {
  703.         return new FieldPVCoordinates<>(position.negate(), velocity.negate(), acceleration.negate());
  704.     }

  706.     /** Normalize the position part of the instance.
  707.      * <p>
  708.      * The computed coordinates first component (position) will be a
  709.      * normalized vector, the second component (velocity) will be the
  710.      * derivative of the first component (hence it will generally not
  711.      * be normalized), and the third component (acceleration) will be the
  712.      * derivative of the second component (hence it will generally not
  713.      * be normalized).
  714.      * </p>
  715.      * @return a new instance, with first component normalized and
  716.      * remaining component computed to have consistent derivatives
  717.      */
  718.     public FieldPVCoordinates<T> normalize() {
  719.         final T   inv     = position.getNorm().reciprocal();
  720.         final FieldVector3D<T> u       = new FieldVector3D<>(inv, position);
  721.         final FieldVector3D<T> v       = new FieldVector3D<>(inv, velocity);
  722.         final FieldVector3D<T> w       = new FieldVector3D<>(inv, acceleration);
  723.         final T   uv      = FieldVector3D.dotProduct(u, v);
  724.         final T   v2      = FieldVector3D.dotProduct(v, v);
  725.         final T   uw      = FieldVector3D.dotProduct(u, w);
  726.         final FieldVector3D<T> uDot    = new FieldVector3D<>(inv.getField().getOne(), v,
  727.                                                              uv.multiply(-1), u);
  728.         final FieldVector3D<T> uDotDot = new FieldVector3D<>(inv.getField().getOne(), w,
  729.                                                              uv.multiply(-2), v,
  730.                                                              uv.multiply(uv).multiply(3).subtract(v2).subtract(uw), u);
  731.         return new FieldPVCoordinates<>(u, uDot, uDotDot);
  732.     }

  734.     /** Compute the cross-product of two instances.
  735.      * @param pv2 second instances
  736.      * @return the cross product v1 ^ v2 as a new instance
  737.      */
  738.     public FieldPVCoordinates<T> crossProduct(final FieldPVCoordinates<T> pv2) {
  739.         final FieldVector3D<T> p1 = position;
  740.         final FieldVector3D<T> v1 = velocity;
  741.         final FieldVector3D<T> a1 = acceleration;
  742.         final FieldVector3D<T> p2 = pv2.position;
  743.         final FieldVector3D<T> v2 = pv2.velocity;
  744.         final FieldVector3D<T> a2 = pv2.acceleration;
  745.         return new FieldPVCoordinates<>(FieldVector3D.crossProduct(p1, p2),
  746.                                         new FieldVector3D<>(1, FieldVector3D.crossProduct(p1, v2),
  747.                                                             1, FieldVector3D.crossProduct(v1, p2)),
  748.                                         new FieldVector3D<>(1, FieldVector3D.crossProduct(p1, a2),
  749.                                                             2, FieldVector3D.crossProduct(v1, v2),
  750.                                                             1, FieldVector3D.crossProduct(a1, p2)));
  751.     }

  753.     /** Convert to a constant position-velocity.
  754.      * @return a constant position-velocity
  755.      */
  756.     public PVCoordinates toPVCoordinates() {
  757.         return new PVCoordinates(position.toVector3D(), velocity.toVector3D(), acceleration.toVector3D());
  758.     }

  760.     /** Return a string representation of this position/velocity pair.
  761.      * @return string representation of this position/velocity pair
  762.      */
  763.     public String toString() {
  764.         final String comma = ", ";
  765.         return new StringBuffer().append('{').append("P(").
  766.                                   append(position.getX().getReal()).append(comma).
  767.                                   append(position.getY().getReal()).append(comma).
  768.                                   append(position.getZ().getReal()).append("), V(").
  769.                                   append(velocity.getX().getReal()).append(comma).
  770.                                   append(velocity.getY().getReal()).append(comma).
  771.                                   append(velocity.getZ().getReal()).append("), A(").
  772.                                   append(acceleration.getX().getReal()).append(comma).
  773.                                   append(acceleration.getY().getReal()).append(comma).
  774.                                   append(acceleration.getZ().getReal()).append(")}").toString();
  775.     }

  777. }
Created with JaCoCo 0.8.6.202009150832