FieldPVCoordinates.java

  1. /* Copyright 2002-2022 CS GROUP
  2.  * Licensed to CS GROUP (CS) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * CS licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *   http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.orekit.utils;

  19. import org.hipparchus.Field;
  20. import org.hipparchus.CalculusFieldElement;
  21. import org.hipparchus.analysis.differentiation.FDSFactory;
  22. import org.hipparchus.analysis.differentiation.FieldDerivative;
  23. import org.hipparchus.analysis.differentiation.FieldDerivativeStructure;
  24. import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative1;
  25. import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative2;
  26. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  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 pairs, using {@link CalculusFieldElement}.
  33.  * <p>
  34.  * The state can be slightly shifted to close dates. This shift is based on
  35.  * a simple linear 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 FieldAngularCoordinates}.
  41.  * </p>
  42.  * <p>Instances of this class are guaranteed to be immutable.</p>
  43.  * @param <T> the type of the field elements
  44.  * @author Luc Maisonobe
  45.  * @since 6.0
  46.  * @see PVCoordinates
  47.  */
  48. public class FieldPVCoordinates<T extends CalculusFieldElement<T>>
  49.     implements TimeShiftable<FieldPVCoordinates<T>> {

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

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

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

  60.     /** Builds a FieldPVCoordinates triplet with zero acceleration.
  61.      * @param position the position vector (m)
  62.      * @param velocity the velocity vector (m/s)
  63.      */
  64.     public FieldPVCoordinates(final FieldVector3D<T> position, final FieldVector3D<T> velocity) {
  65.         this.position     = position;
  66.         this.velocity     = velocity;
  67.         final T zero      = position.getX().getField().getZero();
  68.         this.acceleration = new FieldVector3D<>(zero, zero, zero);
  69.     }

  71.     /** Builds a FieldPVCoordinates triplet.
  72.      * @param position the position vector (m)
  73.      * @param velocity the velocity vector (m/s)
  74.      * @param acceleration the acceleration vector (m/s²)
  75.      */
  76.     public FieldPVCoordinates(final FieldVector3D<T> position, final FieldVector3D<T> velocity,
  77.                               final FieldVector3D<T> acceleration) {
  78.         this.position     = position;
  79.         this.velocity     = velocity;
  80.         this.acceleration = acceleration;
  81.     }

  83.     /** Builds a FieldPVCoordinates from a field and a regular PVCoordinates.
  84.      * @param field field for the components
  85.      * @param pv PVCoordinates triplet to convert
  86.      */
  87.     public FieldPVCoordinates(final Field<T> field, final PVCoordinates pv) {
  88.         this.position     = new FieldVector3D<>(field, pv.getPosition());
  89.         this.velocity     = new FieldVector3D<>(field, pv.getVelocity());
  90.         this.acceleration = new FieldVector3D<>(field, pv.getAcceleration());
  91.     }

  93.     /** Multiplicative constructor.
  94.      * <p>Build a PVCoordinates from another one and a scale factor.</p>
  95.      * <p>The PVCoordinates built will be a * pv</p>
  96.      * @param a scale factor
  97.      * @param pv base (unscaled) PVCoordinates
  98.      */
  99.     public FieldPVCoordinates(final double a, final FieldPVCoordinates<T> pv) {
  100.         position     = new FieldVector3D<>(a, pv.position);
  101.         velocity     = new FieldVector3D<>(a, pv.velocity);
  102.         acceleration = new FieldVector3D<>(a, pv.acceleration);
  103.     }

  105.     /** Multiplicative constructor.
  106.      * <p>Build a PVCoordinates from another one and a scale factor.</p>
  107.      * <p>The PVCoordinates built will be a * pv</p>
  108.      * @param a scale factor
  109.      * @param pv base (unscaled) PVCoordinates
  110.      */
  111.     public FieldPVCoordinates(final T a, final FieldPVCoordinates<T> pv) {
  112.         position     = new FieldVector3D<>(a, pv.position);
  113.         velocity     = new FieldVector3D<>(a, pv.velocity);
  114.         acceleration = new FieldVector3D<>(a, pv.acceleration);
  115.     }

  117.     /** Multiplicative constructor.
  118.      * <p>Build a PVCoordinates from another one and a scale factor.</p>
  119.      * <p>The PVCoordinates built will be a * pv</p>
  120.      * @param a scale factor
  121.      * @param pv base (unscaled) PVCoordinates
  122.      */
  123.     public FieldPVCoordinates(final T a, final PVCoordinates pv) {
  124.         position     = new FieldVector3D<>(a, pv.getPosition());
  125.         velocity     = new FieldVector3D<>(a, pv.getVelocity());
  126.         acceleration = new FieldVector3D<>(a, pv.getAcceleration());
  127.     }

  129.     /** Subtractive constructor.
  130.      * <p>Build a relative PVCoordinates from a start and an end position.</p>
  131.      * <p>The PVCoordinates built will be end - start.</p>
  132.      * @param start Starting PVCoordinates
  133.      * @param end ending PVCoordinates
  134.      */
  135.     public FieldPVCoordinates(final FieldPVCoordinates<T> start, final FieldPVCoordinates<T> end) {
  136.         this.position     = end.position.subtract(start.position);
  137.         this.velocity     = end.velocity.subtract(start.velocity);
  138.         this.acceleration = end.acceleration.subtract(start.acceleration);
  139.     }

  141.     /** Linear constructor.
  142.      * <p>Build a PVCoordinates from two other ones and corresponding scale factors.</p>
  143.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2</p>
  144.      * @param a1 first scale factor
  145.      * @param pv1 first base (unscaled) PVCoordinates
  146.      * @param a2 second scale factor
  147.      * @param pv2 second base (unscaled) PVCoordinates
  148.      */
  149.     public FieldPVCoordinates(final double a1, final FieldPVCoordinates<T> pv1,
  150.                               final double a2, final FieldPVCoordinates<T> pv2) {
  151.         position     = new FieldVector3D<>(a1, pv1.position, a2, pv2.position);
  152.         velocity     = new FieldVector3D<>(a1, pv1.velocity, a2, pv2.velocity);
  153.         acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration);
  154.     }

  156.     /** Linear constructor.
  157.      * <p>Build a PVCoordinates from two other ones and corresponding scale factors.</p>
  158.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2</p>
  159.      * @param a1 first scale factor
  160.      * @param pv1 first base (unscaled) PVCoordinates
  161.      * @param a2 second scale factor
  162.      * @param pv2 second base (unscaled) PVCoordinates
  163.      */
  164.     public FieldPVCoordinates(final T a1, final FieldPVCoordinates<T> pv1,
  165.                               final T a2, final FieldPVCoordinates<T> pv2) {
  166.         position     = new FieldVector3D<>(a1, pv1.position, a2, pv2.position);
  167.         velocity     = new FieldVector3D<>(a1, pv1.velocity, a2, pv2.velocity);
  168.         acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration);
  169.     }

  171.     /** Linear constructor.
  172.      * <p>Build a PVCoordinates from two other ones and corresponding scale factors.</p>
  173.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2</p>
  174.      * @param a1 first scale factor
  175.      * @param pv1 first base (unscaled) PVCoordinates
  176.      * @param a2 second scale factor
  177.      * @param pv2 second base (unscaled) PVCoordinates
  178.      */
  179.     public FieldPVCoordinates(final T a1, final PVCoordinates pv1,
  180.                               final T a2, final PVCoordinates pv2) {
  181.         position     = new FieldVector3D<>(a1, pv1.getPosition(), a2, pv2.getPosition());
  182.         velocity     = new FieldVector3D<>(a1, pv1.getVelocity(), a2, pv2.getVelocity());
  183.         acceleration = new FieldVector3D<>(a1, pv1.getAcceleration(), a2, pv2.getAcceleration());
  184.     }

  186.     /** Linear constructor.
  187.      * <p>Build a PVCoordinates from three other ones and corresponding scale factors.</p>
  188.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3</p>
  189.      * @param a1 first scale factor
  190.      * @param pv1 first base (unscaled) PVCoordinates
  191.      * @param a2 second scale factor
  192.      * @param pv2 second base (unscaled) PVCoordinates
  193.      * @param a3 third scale factor
  194.      * @param pv3 third base (unscaled) PVCoordinates
  195.      */
  196.     public FieldPVCoordinates(final double a1, final FieldPVCoordinates<T> pv1,
  197.                               final double a2, final FieldPVCoordinates<T> pv2,
  198.                               final double a3, final FieldPVCoordinates<T> pv3) {
  199.         position     = new FieldVector3D<>(a1, pv1.position,     a2, pv2.position,     a3, pv3.position);
  200.         velocity     = new FieldVector3D<>(a1, pv1.velocity,     a2, pv2.velocity,     a3, pv3.velocity);
  201.         acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration, a3, pv3.acceleration);
  202.     }

  204.     /** Linear constructor.
  205.      * <p>Build a PVCoordinates from three other ones and corresponding scale factors.</p>
  206.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3</p>
  207.      * @param a1 first scale factor
  208.      * @param pv1 first base (unscaled) PVCoordinates
  209.      * @param a2 second scale factor
  210.      * @param pv2 second base (unscaled) PVCoordinates
  211.      * @param a3 third scale factor
  212.      * @param pv3 third base (unscaled) PVCoordinates
  213.      */
  214.     public FieldPVCoordinates(final T a1, final FieldPVCoordinates<T> pv1,
  215.                               final T a2, final FieldPVCoordinates<T> pv2,
  216.                               final T a3, final FieldPVCoordinates<T> pv3) {
  217.         position     = new FieldVector3D<>(a1, pv1.position,     a2, pv2.position,     a3, pv3.position);
  218.         velocity     = new FieldVector3D<>(a1, pv1.velocity,     a2, pv2.velocity,     a3, pv3.velocity);
  219.         acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration, a3, pv3.acceleration);
  220.     }

  222.     /** Linear constructor.
  223.      * <p>Build a PVCoordinates from three other ones and corresponding scale factors.</p>
  224.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3</p>
  225.      * @param a1 first scale factor
  226.      * @param pv1 first base (unscaled) PVCoordinates
  227.      * @param a2 second scale factor
  228.      * @param pv2 second base (unscaled) PVCoordinates
  229.      * @param a3 third scale factor
  230.      * @param pv3 third base (unscaled) PVCoordinates
  231.      */
  232.     public FieldPVCoordinates(final T a1, final PVCoordinates pv1,
  233.                               final T a2, final PVCoordinates pv2,
  234.                               final T a3, final PVCoordinates pv3) {
  235.         position     = new FieldVector3D<>(a1, pv1.getPosition(),     a2, pv2.getPosition(),     a3, pv3.getPosition());
  236.         velocity     = new FieldVector3D<>(a1, pv1.getVelocity(),     a2, pv2.getVelocity(),     a3, pv3.getVelocity());
  237.         acceleration = new FieldVector3D<>(a1, pv1.getAcceleration(), a2, pv2.getAcceleration(), a3, pv3.getAcceleration());
  238.     }

  240.     /** Linear constructor.
  241.      * <p>Build a PVCoordinates from four other ones and corresponding scale factors.</p>
  242.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4</p>
  243.      * @param a1 first scale factor
  244.      * @param pv1 first base (unscaled) PVCoordinates
  245.      * @param a2 second scale factor
  246.      * @param pv2 second base (unscaled) PVCoordinates
  247.      * @param a3 third scale factor
  248.      * @param pv3 third base (unscaled) PVCoordinates
  249.      * @param a4 fourth scale factor
  250.      * @param pv4 fourth base (unscaled) PVCoordinates
  251.      */
  252.     public FieldPVCoordinates(final double a1, final FieldPVCoordinates<T> pv1,
  253.                               final double a2, final FieldPVCoordinates<T> pv2,
  254.                               final double a3, final FieldPVCoordinates<T> pv3,
  255.                               final double a4, final FieldPVCoordinates<T> pv4) {
  256.         position     = new FieldVector3D<>(a1, pv1.position,     a2, pv2.position,     a3, pv3.position,     a4, pv4.position);
  257.         velocity     = new FieldVector3D<>(a1, pv1.velocity,     a2, pv2.velocity,     a3, pv3.velocity,     a4, pv4.velocity);
  258.         acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration, a3, pv3.acceleration, a4, pv4.acceleration);
  259.     }

  261.     /** Linear constructor.
  262.      * <p>Build a PVCoordinates from four other ones and corresponding scale factors.</p>
  263.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4</p>
  264.      * @param a1 first scale factor
  265.      * @param pv1 first base (unscaled) PVCoordinates
  266.      * @param a2 second scale factor
  267.      * @param pv2 second base (unscaled) PVCoordinates
  268.      * @param a3 third scale factor
  269.      * @param pv3 third base (unscaled) PVCoordinates
  270.      * @param a4 fourth scale factor
  271.      * @param pv4 fourth base (unscaled) PVCoordinates
  272.      */
  273.     public FieldPVCoordinates(final T a1, final FieldPVCoordinates<T> pv1,
  274.                               final T a2, final FieldPVCoordinates<T> pv2,
  275.                               final T a3, final FieldPVCoordinates<T> pv3,
  276.                               final T a4, final FieldPVCoordinates<T> pv4) {
  277.         position     = new FieldVector3D<>(a1, pv1.position,     a2, pv2.position,     a3, pv3.position,     a4, pv4.position);
  278.         velocity     = new FieldVector3D<>(a1, pv1.velocity,     a2, pv2.velocity,     a3, pv3.velocity,     a4, pv4.velocity);
  279.         acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration, a3, pv3.acceleration, a4, pv4.acceleration);
  280.     }

  282.     /** Linear constructor.
  283.      * <p>Build a PVCoordinates from four other ones and corresponding scale factors.</p>
  284.      * <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4</p>
  285.      * @param a1 first scale factor
  286.      * @param pv1 first base (unscaled) PVCoordinates
  287.      * @param a2 second scale factor
  288.      * @param pv2 second base (unscaled) PVCoordinates
  289.      * @param a3 third scale factor
  290.      * @param pv3 third base (unscaled) PVCoordinates
  291.      * @param a4 fourth scale factor
  292.      * @param pv4 fourth base (unscaled) PVCoordinates
  293.      */
  294.     public FieldPVCoordinates(final T a1, final PVCoordinates pv1,
  295.                               final T a2, final PVCoordinates pv2,
  296.                               final T a3, final PVCoordinates pv3,
  297.                               final T a4, final PVCoordinates pv4) {
  298.         position     = new FieldVector3D<>(a1, pv1.getPosition(),     a2, pv2.getPosition(),
  299.                                            a3, pv3.getPosition(),     a4, pv4.getPosition());
  300.         velocity     = new FieldVector3D<>(a1, pv1.getVelocity(),     a2, pv2.getVelocity(),
  301.                                            a3, pv3.getVelocity(),     a4, pv4.getVelocity());
  302.         acceleration = new FieldVector3D<>(a1, pv1.getAcceleration(), a2, pv2.getAcceleration(),
  303.                                            a3, pv3.getAcceleration(), a4, pv4.getAcceleration());
  304.     }

  306.     /** Builds a FieldPVCoordinates triplet from  a {@link FieldVector3D}&lt;{@link FieldDerivativeStructure}&gt;.
  307.      * <p>
  308.      * The vector components must have time as their only derivation parameter and
  309.      * have consistent derivation orders.
  310.      * </p>
  311.      * @param p vector with time-derivatives embedded within the coordinates
  312.      * @param <U> type of the derivative
  313.      * @since 9.2
  314.      */
  315.     public <U extends FieldDerivative<T, U>> FieldPVCoordinates(final FieldVector3D<U> p) {
  316.         position = new FieldVector3D<>(p.getX().getValue(), p.getY().getValue(), p.getZ().getValue());
  317.         if (p.getX().getOrder() >= 1) {
  318.             velocity = new FieldVector3D<>(p.getX().getPartialDerivative(1),
  319.                                            p.getY().getPartialDerivative(1),
  320.                                            p.getZ().getPartialDerivative(1));
  321.             if (p.getX().getOrder() >= 2) {
  322.                 acceleration = new FieldVector3D<>(p.getX().getPartialDerivative(2),
  323.                                                    p.getY().getPartialDerivative(2),
  324.                                                    p.getZ().getPartialDerivative(2));
  325.             } else {
  326.                 acceleration = FieldVector3D.getZero(position.getX().getField());
  327.             }
  328.         } else {
  329.             final FieldVector3D<T> zero = FieldVector3D.getZero(position.getX().getField());
  330.             velocity     = zero;
  331.             acceleration = zero;
  332.         }
  333.     }

  335.     /** Get fixed position/velocity at origin (both p, v and a are zero vectors).
  336.      * @param field field for the components
  337.      * @param <T> the type of the field elements
  338.      * @return a new fixed position/velocity at origin
  339.      */
  340.     public static <T extends CalculusFieldElement<T>> FieldPVCoordinates<T> getZero(final Field<T> field) {
  341.         return new FieldPVCoordinates<>(field, PVCoordinates.ZERO);
  342.     }

  344.     /** Transform the instance to a {@link FieldVector3D}&lt;{@link FieldDerivativeStructure}&gt;.
  345.      * <p>
  346.      * The {@link FieldDerivativeStructure} coordinates correspond to time-derivatives up
  347.      * to the user-specified order.
  348.      * </p>
  349.      * @param order derivation order for the vector components (must be either 0, 1 or 2)
  350.      * @return vector with time-derivatives embedded within the coordinates
  351.           * @since 9.2
  352.      */
  353.     public FieldVector3D<FieldDerivativeStructure<T>> toDerivativeStructureVector(final int order) {

  355.         final FDSFactory<T> factory;
  356.         final FieldDerivativeStructure<T> x;
  357.         final FieldDerivativeStructure<T> y;
  358.         final FieldDerivativeStructure<T> z;
  359.         switch (order) {
  360.             case 0 :
  361.                 factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
  362.                 x = factory.build(position.getX());
  363.                 y = factory.build(position.getY());
  364.                 z = factory.build(position.getZ());
  365.                 break;
  366.             case 1 :
  367.                 factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
  368.                 x = factory.build(position.getX(), velocity.getX());
  369.                 y = factory.build(position.getY(), velocity.getY());
  370.                 z = factory.build(position.getZ(), velocity.getZ());
  371.                 break;
  372.             case 2 :
  373.                 factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
  374.                 x = factory.build(position.getX(), velocity.getX(), acceleration.getX());
  375.                 y = factory.build(position.getY(), velocity.getY(), acceleration.getY());
  376.                 z = factory.build(position.getZ(), velocity.getZ(), acceleration.getZ());
  377.                 break;
  378.             default :
  379.                 throw new OrekitException(OrekitMessages.OUT_OF_RANGE_DERIVATION_ORDER, order);
  380.         }

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

  384.     }

  386.     /** Transform the instance to a {@link FieldVector3D}&lt;{@link FieldUnivariateDerivative1}&gt;.
  387.      * <p>
  388.      * The {@link FieldUnivariateDerivative1} coordinates correspond to time-derivatives up
  389.      * to the order 1.
  390.      * </p>
  391.      * @return vector with time-derivatives embedded within the coordinates
  392.      * @see #toUnivariateDerivative2Vector()
  393.      * @since 10.2
  394.      */
  395.     public FieldVector3D<FieldUnivariateDerivative1<T>> toUnivariateDerivative1Vector() {

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

  401.         return new FieldVector3D<>(x, y, z);
  402.     }

  404.     /** Transform the instance to a {@link FieldVector3D}&lt;{@link FieldUnivariateDerivative2}&gt;.
  405.      * <p>
  406.      * The {@link FieldUnivariateDerivative2} coordinates correspond to time-derivatives up
  407.      * to the order 2.
  408.      * </p>
  409.      * @return vector with time-derivatives embedded within the coordinates
  410.      * @see #toUnivariateDerivative1Vector()
  411.      * @since 10.2
  412.      */
  413.     public FieldVector3D<FieldUnivariateDerivative2<T>> toUnivariateDerivative2Vector() {

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

  419.         return new FieldVector3D<>(x, y, z);
  420.     }

  422.     /** Transform the instance to a {@link FieldPVCoordinates}&lt;{@link FieldDerivativeStructure}&gt;.
  423.      * <p>
  424.      * The {@link FieldDerivativeStructure} coordinates correspond to time-derivatives up
  425.      * to the user-specified order. As both the instance components {@link #getPosition() position},
  426.      * {@link #getVelocity() velocity} and {@link #getAcceleration() acceleration} and the
  427.      * {@link FieldDerivativeStructure#getPartialDerivative(int...) derivatives} of the components
  428.      * holds time-derivatives, there are several ways to retrieve these derivatives. If for example
  429.      * the {@code order} is set to 2, then both {@code pv.getPosition().getX().getPartialDerivative(2)},
  430.      * {@code pv.getVelocity().getX().getPartialDerivative(1)} and
  431.      * {@code pv.getAcceleration().getX().getValue()} return the exact same value.
  432.      * </p>
  433.      * <p>
  434.      * If derivation order is 1, the first derivative of acceleration will be computed as a
  435.      * Keplerian-only jerk. If derivation order is 2, the second derivative of velocity (which
  436.      * is also the first derivative of acceleration) will be computed as a Keplerian-only jerk,
  437.      * and the second derivative of acceleration will be computed as a Keplerian-only jounce.
  438.      * </p>
  439.      * @param order derivation order for the vector components (must be either 0, 1 or 2)
  440.      * @return pv coordinates with time-derivatives embedded within the coordinates
  441.           * @since 9.2
  442.      */
  443.     public FieldPVCoordinates<FieldDerivativeStructure<T>> toDerivativeStructurePV(final int order) {

  445.         final FDSFactory<T> factory;
  446.         final FieldDerivativeStructure<T> x0;
  447.         final FieldDerivativeStructure<T> y0;
  448.         final FieldDerivativeStructure<T> z0;
  449.         final FieldDerivativeStructure<T> x1;
  450.         final FieldDerivativeStructure<T> y1;
  451.         final FieldDerivativeStructure<T> z1;
  452.         final FieldDerivativeStructure<T> x2;
  453.         final FieldDerivativeStructure<T> y2;
  454.         final FieldDerivativeStructure<T> z2;
  455.         switch (order) {
  456.             case 0 :
  457.                 factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
  458.                 x0 = factory.build(position.getX());
  459.                 y0 = factory.build(position.getY());
  460.                 z0 = factory.build(position.getZ());
  461.                 x1 = factory.build(velocity.getX());
  462.                 y1 = factory.build(velocity.getY());
  463.                 z1 = factory.build(velocity.getZ());
  464.                 x2 = factory.build(acceleration.getX());
  465.                 y2 = factory.build(acceleration.getY());
  466.                 z2 = factory.build(acceleration.getZ());
  467.                 break;
  468.             case 1 : {
  469.                 factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
  470.                 final T                r2            = position.getNormSq();
  471.                 final T                r             = r2.sqrt();
  472.                 final T                pvOr2         = FieldVector3D.dotProduct(position, velocity).divide(r2);
  473.                 final T                a             = acceleration.getNorm();
  474.                 final T                aOr           = a.divide(r);
  475.                 final FieldVector3D<T> keplerianJerk = new FieldVector3D<>(pvOr2.multiply(-3), acceleration,
  476.                                                                            aOr.negate(), velocity);
  477.                 x0 = factory.build(position.getX(),     velocity.getX());
  478.                 y0 = factory.build(position.getY(),     velocity.getY());
  479.                 z0 = factory.build(position.getZ(),     velocity.getZ());
  480.                 x1 = factory.build(velocity.getX(),     acceleration.getX());
  481.                 y1 = factory.build(velocity.getY(),     acceleration.getY());
  482.                 z1 = factory.build(velocity.getZ(),     acceleration.getZ());
  483.                 x2 = factory.build(acceleration.getX(), keplerianJerk.getX());
  484.                 y2 = factory.build(acceleration.getY(), keplerianJerk.getY());
  485.                 z2 = factory.build(acceleration.getZ(), keplerianJerk.getZ());
  486.                 break;
  487.             }
  488.             case 2 : {
  489.                 factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
  490.                 final T                r2              = position.getNormSq();
  491.                 final T                r               = r2.sqrt();
  492.                 final T                pvOr2           = FieldVector3D.dotProduct(position, velocity).divide(r2);
  493.                 final T                a               = acceleration.getNorm();
  494.                 final T                aOr             = a.divide(r);
  495.                 final FieldVector3D<T> keplerianJerk   = new FieldVector3D<>(pvOr2.multiply(-3), acceleration,
  496.                                                                              aOr.negate(), velocity);
  497.                 final T                v2              = velocity.getNormSq();
  498.                 final T                pa              = FieldVector3D.dotProduct(position, acceleration);
  499.                 final T                aj              = FieldVector3D.dotProduct(acceleration, keplerianJerk);
  500.                 final FieldVector3D<T> keplerianJounce = new FieldVector3D<>(v2.add(pa).multiply(-3).divide(r2).add(pvOr2.multiply(pvOr2).multiply(15)).subtract(aOr), acceleration,
  501.                                                                              aOr.multiply(4).multiply(pvOr2).subtract(aj.divide(a.multiply(r))), velocity);
  502.                 x0 = factory.build(position.getX(),     velocity.getX(),      acceleration.getX());
  503.                 y0 = factory.build(position.getY(),     velocity.getY(),      acceleration.getY());
  504.                 z0 = factory.build(position.getZ(),     velocity.getZ(),      acceleration.getZ());
  505.                 x1 = factory.build(velocity.getX(),     acceleration.getX(),  keplerianJerk.getX());
  506.                 y1 = factory.build(velocity.getY(),     acceleration.getY(),  keplerianJerk.getY());
  507.                 z1 = factory.build(velocity.getZ(),     acceleration.getZ(),  keplerianJerk.getZ());
  508.                 x2 = factory.build(acceleration.getX(), keplerianJerk.getX(), keplerianJounce.getX());
  509.                 y2 = factory.build(acceleration.getY(), keplerianJerk.getY(), keplerianJounce.getY());
  510.                 z2 = factory.build(acceleration.getZ(), keplerianJerk.getZ(), keplerianJounce.getZ());
  511.                 break;
  512.             }
  513.             default :
  514.                 throw new OrekitException(OrekitMessages.OUT_OF_RANGE_DERIVATION_ORDER, order);
  515.         }

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

  521.     }


  524.     /** Transform the instance to a {@link FieldPVCoordinates}&lt;{@link FieldUnivariateDerivative1}&gt;.
  525.      * <p>
  526.      * The {@link FieldUnivariateDerivative1} coordinates correspond to time-derivatives up
  527.      * to the order 1.
  528.      * The first derivative of acceleration will be computed as a Keplerian-only jerk.
  529.      * </p>
  530.      * @return pv coordinates with time-derivatives embedded within the coordinates
  531.      * @since 10.2
  532.      */
  533.     public FieldPVCoordinates<FieldUnivariateDerivative1<T>> toUnivariateDerivative1PV() {

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

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

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

  557.     }

  559.     /** Transform the instance to a {@link FieldPVCoordinates}&lt;{@link FieldUnivariateDerivative2}&gt;.
  560.      * <p>
  561.      * The {@link FieldUnivariateDerivative2} coordinates correspond to time-derivatives up
  562.      * to the order 2.
  563.      * As derivation order is 2, the second derivative of velocity (which
  564.      * is also the first derivative of acceleration) will be computed as a Keplerian-only jerk,
  565.      * and the second derivative of acceleration will be computed as a Keplerian-only jounce.
  566.      * </p>
  567.      * @return pv coordinates with time-derivatives embedded within the coordinates
  568.      * @since 10.2
  569.      */
  570.     public FieldPVCoordinates<FieldUnivariateDerivative2<T>> toUnivariateDerivative2PV() {

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

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

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

  599.     }

  601.     /** Estimate velocity between two positions.
  602.      * <p>Estimation is based on a simple fixed velocity translation
  603.      * during the time interval between the two positions.</p>
  604.      * @param start start position
  605.      * @param end end position
  606.      * @param dt time elapsed between the dates of the two positions
  607.      * @param <T> the type of the field elements
  608.      * @return velocity allowing to go from start to end positions
  609.      */
  610.     public static <T extends CalculusFieldElement<T>> FieldVector3D<T> estimateVelocity(final FieldVector3D<T> start,
  611.                                                                                     final FieldVector3D<T> end,
  612.                                                                                     final double dt) {
  613.         final double scale = 1.0 / dt;
  614.         return new FieldVector3D<>(scale, end, -scale, start);
  615.     }

  617.     /** Get a time-shifted state.
  618.      * <p>
  619.      * The state can be slightly shifted to close dates. This shift is based on
  620.      * a simple quadratic model. It is <em>not</em> intended as a replacement for
  621.      * proper orbit propagation (it is not even Keplerian!) but should be sufficient
  622.      * for either small time shifts or coarse accuracy.
  623.      * </p>
  624.      * @param dt time shift in seconds
  625.      * @return a new state, shifted with respect to the instance (which is immutable)
  626.      */
  627.     public FieldPVCoordinates<T> shiftedBy(final double dt) {
  628.         return new FieldPVCoordinates<>(new FieldVector3D<>(1, position, dt, velocity, 0.5 * dt * dt, acceleration),
  629.                                         new FieldVector3D<>(1, velocity, dt, acceleration),
  630.                                         acceleration);
  631.     }

  633.     /** Get a time-shifted state.
  634.      * <p>
  635.      * The state can be slightly shifted to close dates. This shift is based on
  636.      * a simple quadratic model. It is <em>not</em> intended as a replacement for
  637.      * proper orbit propagation (it is not even Keplerian!) but should be sufficient
  638.      * for either small time shifts or coarse accuracy.
  639.      * </p>
  640.      * @param dt time shift in seconds
  641.      * @return a new state, shifted with respect to the instance (which is immutable)
  642.      */
  643.     public FieldPVCoordinates<T> shiftedBy(final T dt) {
  644.         final T one = dt.getField().getOne();
  645.         return new FieldPVCoordinates<>(new FieldVector3D<>(one, position,
  646.                                                             dt, velocity,
  647.                                                             dt.multiply(dt).multiply(0.5), acceleration),
  648.                                         new FieldVector3D<>(one, velocity,
  649.                                                             dt, acceleration),
  650.                                         acceleration);
  651.     }

  653.     /** Gets the position.
  654.      * @return the position vector (m).
  655.      */
  656.     public FieldVector3D<T> getPosition() {
  657.         return position;
  658.     }

  660.     /** Gets the velocity.
  661.      * @return the velocity vector (m/s).
  662.      */
  663.     public FieldVector3D<T> getVelocity() {
  664.         return velocity;
  665.     }

  667.     /** Gets the acceleration.
  668.      * @return the acceleration vector (m/s²).
  669.      */
  670.     public FieldVector3D<T> getAcceleration() {
  671.         return acceleration;
  672.     }

  674.     /** Gets the momentum.
  675.      * <p>This vector is the p &otimes; v where p is position, v is velocity
  676.      * and &otimes; is cross product. To get the real physical angular momentum
  677.      * you need to multiply this vector by the mass.</p>
  678.      * <p>The returned vector is recomputed each time this method is called, it
  679.      * is not cached.</p>
  680.      * @return a new instance of the momentum vector (m²/s).
  681.      */
  682.     public FieldVector3D<T> getMomentum() {
  683.         return FieldVector3D.crossProduct(position, velocity);
  684.     }

  686.     /**
  687.      * Get the angular velocity (spin) of this point as seen from the origin.
  688.      *
  689.      * <p> The angular velocity vector is parallel to the {@link #getMomentum()
  690.      * angular * momentum} and is computed by ω = p &times; v / ||p||²
  691.      *
  692.      * @return the angular velocity vector
  693.      * @see <a href="http://en.wikipedia.org/wiki/Angular_velocity">Angular Velocity on
  694.      *      Wikipedia</a>
  695.      */
  696.     public FieldVector3D<T> getAngularVelocity() {
  697.         return this.getMomentum().scalarMultiply(
  698.                 this.getPosition().getNormSq().reciprocal());
  699.     }

  701.     /** Get the opposite of the instance.
  702.      * @return a new position-velocity which is opposite to the instance
  703.      */
  704.     public FieldPVCoordinates<T> negate() {
  705.         return new FieldPVCoordinates<>(position.negate(), velocity.negate(), acceleration.negate());
  706.     }

  708.     /** Normalize the position part of the instance.
  709.      * <p>
  710.      * The computed coordinates first component (position) will be a
  711.      * normalized vector, the second component (velocity) will be the
  712.      * derivative of the first component (hence it will generally not
  713.      * be normalized), and the third component (acceleration) will be the
  714.      * derivative of the second component (hence it will generally not
  715.      * be normalized).
  716.      * </p>
  717.      * @return a new instance, with first component normalized and
  718.      * remaining component computed to have consistent derivatives
  719.      */
  720.     public FieldPVCoordinates<T> normalize() {
  721.         final T   inv     = position.getNorm().reciprocal();
  722.         final FieldVector3D<T> u       = new FieldVector3D<>(inv, position);
  723.         final FieldVector3D<T> v       = new FieldVector3D<>(inv, velocity);
  724.         final FieldVector3D<T> w       = new FieldVector3D<>(inv, acceleration);
  725.         final T   uv      = FieldVector3D.dotProduct(u, v);
  726.         final T   v2      = FieldVector3D.dotProduct(v, v);
  727.         final T   uw      = FieldVector3D.dotProduct(u, w);
  728.         final FieldVector3D<T> uDot    = new FieldVector3D<>(inv.getField().getOne(), v,
  729.                                                              uv.multiply(-1), u);
  730.         final FieldVector3D<T> uDotDot = new FieldVector3D<>(inv.getField().getOne(), w,
  731.                                                              uv.multiply(-2), v,
  732.                                                              uv.multiply(uv).multiply(3).subtract(v2).subtract(uw), u);
  733.         return new FieldPVCoordinates<>(u, uDot, uDotDot);
  734.     }

  736.     /** Compute the cross-product of two instances.
  737.      * @param pv2 second instances
  738.      * @return the cross product v1 ^ v2 as a new instance
  739.      */
  740.     public FieldPVCoordinates<T> crossProduct(final FieldPVCoordinates<T> pv2) {
  741.         final FieldVector3D<T> p1 = position;
  742.         final FieldVector3D<T> v1 = velocity;
  743.         final FieldVector3D<T> a1 = acceleration;
  744.         final FieldVector3D<T> p2 = pv2.position;
  745.         final FieldVector3D<T> v2 = pv2.velocity;
  746.         final FieldVector3D<T> a2 = pv2.acceleration;
  747.         return new FieldPVCoordinates<>(FieldVector3D.crossProduct(p1, p2),
  748.                                         new FieldVector3D<>(1, FieldVector3D.crossProduct(p1, v2),
  749.                                                             1, FieldVector3D.crossProduct(v1, p2)),
  750.                                         new FieldVector3D<>(1, FieldVector3D.crossProduct(p1, a2),
  751.                                                             2, FieldVector3D.crossProduct(v1, v2),
  752.                                                             1, FieldVector3D.crossProduct(a1, p2)));
  753.     }

  755.     /** Convert to a constant position-velocity.
  756.      * @return a constant position-velocity
  757.      */
  758.     public PVCoordinates toPVCoordinates() {
  759.         return new PVCoordinates(position.toVector3D(), velocity.toVector3D(), acceleration.toVector3D());
  760.     }

  762.     /** Return a string representation of this position/velocity pair.
  763.      * @return string representation of this position/velocity pair
  764.      */
  765.     public String toString() {
  766.         final String comma = ", ";
  767.         return new StringBuilder().append('{').append("P(").
  768.                                   append(position.getX().getReal()).append(comma).
  769.                                   append(position.getY().getReal()).append(comma).
  770.                                   append(position.getZ().getReal()).append("), V(").
  771.                                   append(velocity.getX().getReal()).append(comma).
  772.                                   append(velocity.getY().getReal()).append(comma).
  773.                                   append(velocity.getZ().getReal()).append("), A(").
  774.                                   append(acceleration.getX().getReal()).append(comma).
  775.                                   append(acceleration.getY().getReal()).append(comma).
  776.                                   append(acceleration.getZ().getReal()).append(")}").toString();
  777.     }

  779. }
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