PVCoordinates.java

  1. /* Copyright 2002-2017 CS Systèmes d'Information
  2.  * Licensed to CS Systèmes d'Information (CS) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * CS licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *   http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.orekit.utils;

  19. import java.io.Serializable;

  21. import org.hipparchus.analysis.differentiation.DSFactory;
  22. import org.hipparchus.analysis.differentiation.DerivativeStructure;
  23. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  24. import org.hipparchus.geometry.euclidean.threed.Vector3D;
  25. import org.orekit.errors.OrekitException;
  26. import org.orekit.errors.OrekitMessages;
  27. import org.orekit.time.TimeShiftable;

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

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

  48.     /** Serializable UID. */
  49.     private static final long serialVersionUID = 20140407L;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  239.     }

  241.     /** Estimate velocity between two positions.
  242.      * <p>Estimation is based on a simple fixed velocity translation
  243.      * during the time interval between the two positions.</p>
  244.      * @param start start position
  245.      * @param end end position
  246.      * @param dt time elapsed between the dates of the two positions
  247.      * @return velocity allowing to go from start to end positions
  248.      */
  249.     public static Vector3D estimateVelocity(final Vector3D start, final Vector3D end, final double dt) {
  250.         final double scale = 1.0 / dt;
  251.         return new Vector3D(scale, end, -scale, start);
  252.     }

  254.     /** Get a time-shifted state.
  255.      * <p>
  256.      * The state can be slightly shifted to close dates. This shift is based on
  257.      * a simple Taylor expansion. It is <em>not</em> intended as a replacement for
  258.      * proper orbit propagation (it is not even Keplerian!) but should be sufficient
  259.      * for either small time shifts or coarse accuracy.
  260.      * </p>
  261.      * @param dt time shift in seconds
  262.      * @return a new state, shifted with respect to the instance (which is immutable)
  263.      */
  264.     public PVCoordinates shiftedBy(final double dt) {
  265.         return new PVCoordinates(new Vector3D(1, position, dt, velocity, 0.5 * dt * dt, acceleration),
  266.                                  new Vector3D(1, velocity, dt, acceleration),
  267.                                  acceleration);
  268.     }

  270.     /** Gets the position.
  271.      * @return the position vector (m).
  272.      */
  273.     public Vector3D getPosition() {
  274.         return position;
  275.     }

  277.     /** Gets the velocity.
  278.      * @return the velocity vector (m/s).
  279.      */
  280.     public Vector3D getVelocity() {
  281.         return velocity;
  282.     }

  284.     /** Gets the acceleration.
  285.      * @return the acceleration vector (m/s²).
  286.      */
  287.     public Vector3D getAcceleration() {
  288.         return acceleration;
  289.     }

  291.     /** Gets the momentum.
  292.      * <p>This vector is the p &otimes; v where p is position, v is velocity
  293.      * and &otimes; is cross product. To get the real physical angular momentum
  294.      * you need to multiply this vector by the mass.</p>
  295.      * <p>The returned vector is recomputed each time this method is called, it
  296.      * is not cached.</p>
  297.      * @return a new instance of the momentum vector (m²/s).
  298.      */
  299.     public Vector3D getMomentum() {
  300.         return Vector3D.crossProduct(position, velocity);
  301.     }

  303.     /**
  304.      * Get the angular velocity (spin) of this point as seen from the origin.
  305.      *
  306.      * <p> The angular velocity vector is parallel to the {@link #getMomentum()
  307.      * angular momentum} and is computed by ω = p &times; v / ||p||²
  308.      *
  309.      * @return the angular velocity vector
  310.      * @see <a href="http://en.wikipedia.org/wiki/Angular_velocity">Angular Velocity on
  311.      *      Wikipedia</a>
  312.      */
  313.     public Vector3D getAngularVelocity() {
  314.         return this.getMomentum().scalarMultiply(1.0 / this.getPosition().getNormSq());
  315.     }

  317.     /** Get the opposite of the instance.
  318.      * @return a new position-velocity which is opposite to the instance
  319.      */
  320.     public PVCoordinates negate() {
  321.         return new PVCoordinates(position.negate(), velocity.negate(), acceleration.negate());
  322.     }

  324.     /** Normalize the position part of the instance.
  325.      * <p>
  326.      * The computed coordinates first component (position) will be a
  327.      * normalized vector, the second component (velocity) will be the
  328.      * derivative of the first component (hence it will generally not
  329.      * be normalized), and the third component (acceleration) will be the
  330.      * derivative of the second component (hence it will generally not
  331.      * be normalized).
  332.      * </p>
  333.      * @return a new instance, with first component normalized and
  334.      * remaining component computed to have consistent derivatives
  335.      */
  336.     public PVCoordinates normalize() {
  337.         final double   inv     = 1.0 / position.getNorm();
  338.         final Vector3D u       = new Vector3D(inv, position);
  339.         final Vector3D v       = new Vector3D(inv, velocity);
  340.         final Vector3D w       = new Vector3D(inv, acceleration);
  341.         final double   uv      = Vector3D.dotProduct(u, v);
  342.         final double   v2      = Vector3D.dotProduct(v, v);
  343.         final double   uw      = Vector3D.dotProduct(u, w);
  344.         final Vector3D uDot    = new Vector3D(1, v, -uv, u);
  345.         final Vector3D uDotDot = new Vector3D(1, w, -2 * uv, v, 3 * uv * uv - v2 - uw, u);
  346.         return new PVCoordinates(u, uDot, uDotDot);
  347.     }

  349.     /** Compute the cross-product of two instances.
  350.      * @param pv1 first instances
  351.      * @param pv2 second instances
  352.      * @return the cross product v1 ^ v2 as a new instance
  353.      */
  354.     public static PVCoordinates crossProduct(final PVCoordinates pv1, final PVCoordinates pv2) {
  355.         final Vector3D p1 = pv1.position;
  356.         final Vector3D v1 = pv1.velocity;
  357.         final Vector3D a1 = pv1.acceleration;
  358.         final Vector3D p2 = pv2.position;
  359.         final Vector3D v2 = pv2.velocity;
  360.         final Vector3D a2 = pv2.acceleration;
  361.         return new PVCoordinates(Vector3D.crossProduct(p1, p2),
  362.                                  new Vector3D(1, Vector3D.crossProduct(p1, v2),
  363.                                               1, Vector3D.crossProduct(v1, p2)),
  364.                                  new Vector3D(1, Vector3D.crossProduct(p1, a2),
  365.                                               2, Vector3D.crossProduct(v1, v2),
  366.                                               1, Vector3D.crossProduct(a1, p2)));
  367.     }

  369.     /** Return a string representation of this position/velocity pair.
  370.      * @return string representation of this position/velocity pair
  371.      */
  372.     public String toString() {
  373.         final String comma = ", ";
  374.         return new StringBuffer().append('{').append("P(").
  375.                 append(position.getX()).append(comma).
  376.                 append(position.getY()).append(comma).
  377.                 append(position.getZ()).append("), V(").
  378.                 append(velocity.getX()).append(comma).
  379.                 append(velocity.getY()).append(comma).
  380.                 append(velocity.getZ()).append("), A(").
  381.                 append(acceleration.getX()).append(comma).
  382.                 append(acceleration.getY()).append(comma).
  383.                 append(acceleration.getZ()).append(")}").toString();
  384.     }

  386.     /** Replace the instance with a data transfer object for serialization.
  387.      * @return data transfer object that will be serialized
  388.      */
  389.     private Object writeReplace() {
  390.         return new DTO(this);
  391.     }

  393.     /** Internal class used only for serialization. */
  394.     private static class DTO implements Serializable {

  396.         /** Serializable UID. */
  397.         private static final long serialVersionUID = 20140723L;

  399.         /** Double values. */
  400.         private double[] d;

  402.         /** Simple constructor.
  403.          * @param pv instance to serialize
  404.          */
  405.         private DTO(final PVCoordinates pv) {
  406.             this.d = new double[] {
  407.                 pv.getPosition().getX(),     pv.getPosition().getY(),     pv.getPosition().getZ(),
  408.                 pv.getVelocity().getX(),     pv.getVelocity().getY(),     pv.getVelocity().getZ(),
  409.                 pv.getAcceleration().getX(), pv.getAcceleration().getY(), pv.getAcceleration().getZ(),
  410.             };
  411.         }

  413.         /** Replace the deserialized data transfer object with a {@link PVCoordinates}.
  414.          * @return replacement {@link PVCoordinates}
  415.          */
  416.         private Object readResolve() {
  417.             return new PVCoordinates(new Vector3D(d[0], d[1], d[2]),
  418.                                      new Vector3D(d[3], d[4], d[5]),
  419.                                      new Vector3D(d[6], d[7], d[8]));
  420.         }

  422.     }

  424. }
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