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;
18  
19  import java.io.Serializable;
20  
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;
28  
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 {
44  
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);
47  
48      /** Serializable UID. */
49      private static final long serialVersionUID = 20140407L;
50  
51      /** The position. */
52      private final Vector3D position;
53  
54      /** The velocity. */
55      private final Vector3D velocity;
56  
57      /** The acceleration. */
58      private final Vector3D acceleration;
59  
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      }
68  
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      }
79  
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      }
90  
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     }
102 
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     }
114 
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     }
129 
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     }
147 
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     }
171 
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     }
197 
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 {
209 
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         }
236 
237         return new FieldVector3D<>(x, y, z);
238 
239     }
240 
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     }
253 
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     }
269 
270     /** Gets the position.
271      * @return the position vector (m).
272      */
273     public Vector3D getPosition() {
274         return position;
275     }
276 
277     /** Gets the velocity.
278      * @return the velocity vector (m/s).
279      */
280     public Vector3D getVelocity() {
281         return velocity;
282     }
283 
284     /** Gets the acceleration.
285      * @return the acceleration vector (m/s²).
286      */
287     public Vector3D getAcceleration() {
288         return acceleration;
289     }
290 
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     }
302 
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     }
316 
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     }
323 
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     }
348 
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     }
368 
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     }
385 
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     }
392 
393     /** Internal class used only for serialization. */
394     private static class DTO implements Serializable {
395 
396         /** Serializable UID. */
397         private static final long serialVersionUID = 20140723L;
398 
399         /** Double values. */
400         private double[] d;
401 
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         }
412 
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         }
421 
422     }
423 
424 }