1   /* Copyright 2002-2025 CS GROUP
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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
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14   * See the License for the specific language governing permissions and
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17  package org.orekit.utils;
18  
19  import org.hipparchus.CalculusFieldElement;
20  import org.hipparchus.Field;
21  import org.hipparchus.analysis.differentiation.DSFactory;
22  import org.hipparchus.analysis.differentiation.DerivativeStructure;
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.FieldRotation;
27  import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
28  import org.hipparchus.geometry.euclidean.threed.Rotation;
29  import org.hipparchus.geometry.euclidean.threed.RotationConvention;
30  import org.hipparchus.geometry.euclidean.threed.Vector3D;
31  import org.hipparchus.random.RandomGenerator;
32  import org.hipparchus.random.Well1024a;
33  import org.hipparchus.util.Binary64;
34  import org.hipparchus.util.Binary64Field;
35  import org.hipparchus.util.FastMath;
36  import org.junit.jupiter.api.Assertions;
37  import org.junit.jupiter.api.BeforeEach;
38  import org.junit.jupiter.api.Test;
39  import org.orekit.Utils;
40  import org.orekit.time.AbsoluteDate;
41  import org.orekit.time.FieldAbsoluteDate;
42  import org.orekit.time.FieldTimeStamped;
43  
44  import java.util.Random;
45  
46  public class TimeStampedFieldAngularCoordinatesTest {
47  
48      @Test
49      public void testZeroRate() {
50          TimeStampedFieldAngularCoordinates<DerivativeStructure> angularCoordinates =
51                  new TimeStampedFieldAngularCoordinates<>(AbsoluteDate.J2000_EPOCH,
52                                                           createRotation(0.48, 0.64, 0.36, 0.48, false),
53                                                           createVector(0, 0, 0, 4),
54                                                           createVector(0, 0, 0, 4));
55          Assertions.assertEquals(createVector(0, 0, 0, 4), angularCoordinates.getRotationRate());
56          double dt = 10.0;
57          TimeStampedFieldAngularCoordinates<DerivativeStructure> shifted = angularCoordinates.shiftedBy(dt);
58          Assertions.assertEquals(0.0, shifted.getRotationAcceleration().getNorm().getReal(), 1.0e-15);
59          Assertions.assertEquals(0.0, shifted.getRotationRate().getNorm().getReal(), 1.0e-15);
60          Assertions.assertEquals(0.0, FieldRotation.distance(angularCoordinates.getRotation(), shifted.getRotation()).getReal(), 1.0e-15);
61      }
62  
63      @Test
64      public void testShift() {
65          double rate = 2 * FastMath.PI / (12 * 60);
66          TimeStampedFieldAngularCoordinates<DerivativeStructure> angularCoordinates =
67                  new TimeStampedFieldAngularCoordinates<>(AbsoluteDate.J2000_EPOCH,
68                                                           createRotation(1, 0, 0, 0, false),
69                                                           new FieldVector3D<>(rate, createVector(0, 0, 1, 4)),
70                                                           createVector(0, 0, 0, 4));
71          Assertions.assertEquals(rate, angularCoordinates.getRotationRate().getNorm().getReal(), 1.0e-10);
72          double dt = 10.0;
73          double alpha = rate * dt;
74          TimeStampedFieldAngularCoordinates<DerivativeStructure> shifted = angularCoordinates.shiftedBy(dt);
75          Assertions.assertEquals(rate, shifted.getRotationRate().getNorm().getReal(), 1.0e-10);
76          Assertions.assertEquals(alpha, FieldRotation.distance(angularCoordinates.getRotation(), shifted.getRotation()).getReal(), 1.0e-10);
77  
78          FieldVector3D<DerivativeStructure> xSat = shifted.getRotation().applyInverseTo(createVector(1, 0, 0, 4));
79          Assertions.assertEquals(0.0, xSat.subtract(createVector(FastMath.cos(alpha), FastMath.sin(alpha), 0, 4)).getNorm().getReal(), 1.0e-10);
80          FieldVector3D<DerivativeStructure> ySat = shifted.getRotation().applyInverseTo(createVector(0, 1, 0, 4));
81          Assertions.assertEquals(0.0, ySat.subtract(createVector(-FastMath.sin(alpha), FastMath.cos(alpha), 0, 4)).getNorm().getReal(), 1.0e-10);
82          FieldVector3D<DerivativeStructure> zSat = shifted.getRotation().applyInverseTo(createVector(0, 0, 1, 4));
83          Assertions.assertEquals(0.0, zSat.subtract(createVector(0, 0, 1, 4)).getNorm().getReal(), 1.0e-10);
84  
85      }
86  
87      @Test
88      public void testToAC() {
89          Random random = new Random(0xc9b4cf6c371108e0l);
90          for (int i = 0; i < 100; ++i) {
91              FieldRotation<DerivativeStructure> r = randomRotation(random);
92              FieldVector3D<DerivativeStructure> o = randomVector(random, 1.0e-3);
93              FieldVector3D<DerivativeStructure> a = randomVector(random, 1.0e-3);
94              TimeStampedFieldAngularCoordinates<DerivativeStructure> acds =
95          new TimeStampedFieldAngularCoordinates<>(AbsoluteDate.J2000_EPOCH, r, o, a);
96              AngularCoordinates ac = acds.toAngularCoordinates();
97              Assertions.assertEquals(0, Rotation.distance(r.toRotation(), ac.getRotation()), 1.0e-15);
98              Assertions.assertEquals(0, FieldVector3D.distance(o, ac.getRotationRate()).getReal(), 1.0e-15);
99              Assertions.assertEquals(0, FieldVector3D.distance(a, ac.getRotationAcceleration()).getReal(), 1.0e-15);
100         }
101     }
102 
103     @Test
104     public void testSpin() {
105         double rate = 2 * FastMath.PI / (12 * 60);
106         TimeStampedFieldAngularCoordinates<DerivativeStructure> angularCoordinates =
107                 new TimeStampedFieldAngularCoordinates<>(AbsoluteDate.J2000_EPOCH,
108                                                          createRotation(0.48, 0.64, 0.36, 0.48, false),
109                                                          new FieldVector3D<>(rate, createVector(0, 0, 1, 4)),
110                                         createVector(0, 0, 0, 4));
111         Assertions.assertEquals(rate, angularCoordinates.getRotationRate().getNorm().getReal(), 1.0e-10);
112         double dt = 10.0;
113         TimeStampedFieldAngularCoordinates<DerivativeStructure> shifted = angularCoordinates.shiftedBy(dt);
114         Assertions.assertEquals(rate, shifted.getRotationRate().getNorm().getReal(), 1.0e-10);
115         Assertions.assertEquals(rate * dt, FieldRotation.distance(angularCoordinates.getRotation(), shifted.getRotation()).getReal(), 1.0e-10);
116 
117         FieldVector3D<DerivativeStructure> shiftedX  = shifted.getRotation().applyInverseTo(createVector(1, 0, 0, 4));
118         FieldVector3D<DerivativeStructure> shiftedY  = shifted.getRotation().applyInverseTo(createVector(0, 1, 0, 4));
119         FieldVector3D<DerivativeStructure> shiftedZ  = shifted.getRotation().applyInverseTo(createVector(0, 0, 1, 4));
120         FieldVector3D<DerivativeStructure> originalX = angularCoordinates.getRotation().applyInverseTo(createVector(1, 0, 0, 4));
121         FieldVector3D<DerivativeStructure> originalY = angularCoordinates.getRotation().applyInverseTo(createVector(0, 1, 0, 4));
122         FieldVector3D<DerivativeStructure> originalZ = angularCoordinates.getRotation().applyInverseTo(createVector(0, 0, 1, 4));
123         Assertions.assertEquals( FastMath.cos(rate * dt), FieldVector3D.dotProduct(shiftedX, originalX).getReal(), 1.0e-10);
124         Assertions.assertEquals( FastMath.sin(rate * dt), FieldVector3D.dotProduct(shiftedX, originalY).getReal(), 1.0e-10);
125         Assertions.assertEquals( 0.0,                 FieldVector3D.dotProduct(shiftedX, originalZ).getReal(), 1.0e-10);
126         Assertions.assertEquals(-FastMath.sin(rate * dt), FieldVector3D.dotProduct(shiftedY, originalX).getReal(), 1.0e-10);
127         Assertions.assertEquals( FastMath.cos(rate * dt), FieldVector3D.dotProduct(shiftedY, originalY).getReal(), 1.0e-10);
128         Assertions.assertEquals( 0.0,                 FieldVector3D.dotProduct(shiftedY, originalZ).getReal(), 1.0e-10);
129         Assertions.assertEquals( 0.0,                 FieldVector3D.dotProduct(shiftedZ, originalX).getReal(), 1.0e-10);
130         Assertions.assertEquals( 0.0,                 FieldVector3D.dotProduct(shiftedZ, originalY).getReal(), 1.0e-10);
131         Assertions.assertEquals( 1.0,                 FieldVector3D.dotProduct(shiftedZ, originalZ).getReal(), 1.0e-10);
132 
133         FieldVector3D<DerivativeStructure> forward = FieldAngularCoordinates.estimateRate(angularCoordinates.getRotation(), shifted.getRotation(), dt);
134         Assertions.assertEquals(0.0, forward.subtract(angularCoordinates.getRotationRate()).getNorm().getReal(), 1.0e-10);
135 
136         FieldVector3D<DerivativeStructure> reversed = FieldAngularCoordinates.estimateRate(shifted.getRotation(), angularCoordinates.getRotation(), dt);
137         Assertions.assertEquals(0.0, reversed.add(angularCoordinates.getRotationRate()).getNorm().getReal(), 1.0e-10);
138 
139     }
140 
141     @Test
142     public void testReverseOffset() {
143         Random random = new Random(0x4ecca9d57a8f1611l);
144         for (int i = 0; i < 100; ++i) {
145             FieldRotation<DerivativeStructure> r = randomRotation(random);
146             FieldVector3D<DerivativeStructure> o = randomVector(random, 1.0e-3);
147             FieldVector3D<DerivativeStructure> a = randomVector(random, 1.0e-3);
148             TimeStampedFieldAngularCoordinates<DerivativeStructure> ac =
149         new TimeStampedFieldAngularCoordinates<>(AbsoluteDate.J2000_EPOCH, r, o, a);
150             TimeStampedFieldAngularCoordinates<DerivativeStructure> sum = ac.addOffset(ac.revert());
151             Assertions.assertEquals(0.0, sum.getRotation().getAngle().getReal(), 1.0e-15);
152             Assertions.assertEquals(0.0, sum.getRotationRate().getNorm().getReal(), 1.0e-15);
153             Assertions.assertEquals(0.0, sum.getRotationAcceleration().getNorm().getReal(), 1.0e-15);
154         }
155     }
156 
157     @Test
158     public void testNoCommute() {
159         TimeStampedFieldAngularCoordinates<DerivativeStructure> ac1 =
160                 new TimeStampedFieldAngularCoordinates<>(AbsoluteDate.J2000_EPOCH,
161                                                          createRotation(0.48,  0.64, 0.36, 0.48, false),
162                                                          createVector(0, 0, 0, 4),
163                                                          createVector(0, 0, 0, 4));
164         TimeStampedFieldAngularCoordinates<DerivativeStructure> ac2 =
165                 new TimeStampedFieldAngularCoordinates<>(AbsoluteDate.J2000_EPOCH,
166                                                          createRotation(0.36, -0.48, 0.48, 0.64, false),
167                                                          createVector(0, 0, 0, 4),
168                                                          createVector(0, 0, 0, 4));
169 
170         TimeStampedFieldAngularCoordinates<DerivativeStructure> add12 = ac1.addOffset(ac2);
171         TimeStampedFieldAngularCoordinates<DerivativeStructure> add21 = ac2.addOffset(ac1);
172 
173         // the rotations are really different from each other
174         Assertions.assertEquals(2.574, FieldRotation.distance(add12.getRotation(), add21.getRotation()).getReal(), 1.0e-3);
175 
176     }
177 
178     @Test
179     public void testRoundTripNoOp() {
180         Random random = new Random(0x1e610cfe89306669l);
181         for (int i = 0; i < 100; ++i) {
182 
183             FieldRotation<DerivativeStructure> r1 = randomRotation(random);
184             FieldVector3D<DerivativeStructure> o1 = randomVector(random, 1.0e-2);
185             FieldVector3D<DerivativeStructure> a1 = randomVector(random, 1.0e-2);
186             TimeStampedFieldAngularCoordinates<DerivativeStructure> ac1 =
187         new TimeStampedFieldAngularCoordinates<>(AbsoluteDate.J2000_EPOCH, r1, o1, a1);
188             FieldRotation<DerivativeStructure> r2 = randomRotation(random);
189             FieldVector3D<DerivativeStructure> o2 = randomVector(random, 1.0e-2);
190             FieldVector3D<DerivativeStructure> a2 = randomVector(random, 1.0e-2);
191 
192             TimeStampedFieldAngularCoordinates<DerivativeStructure> ac2 =
193         new TimeStampedFieldAngularCoordinates<>(AbsoluteDate.J2000_EPOCH, r2, o2, a2);
194             TimeStampedFieldAngularCoordinates<DerivativeStructure> roundTripSA = ac1.subtractOffset(ac2).addOffset(ac2);
195             Assertions.assertEquals(0.0, FieldRotation.distance(ac1.getRotation(), roundTripSA.getRotation()).getReal(), 4.0e-16);
196             Assertions.assertEquals(0.0, FieldVector3D.distance(ac1.getRotationRate(), roundTripSA.getRotationRate()).getReal(), 2.0e-17);
197             Assertions.assertEquals(0.0, FieldVector3D.distance(ac1.getRotationAcceleration(), roundTripSA.getRotationAcceleration()).getReal(), 1.0e-17);
198 
199             TimeStampedFieldAngularCoordinates<DerivativeStructure> roundTripAS = ac1.addOffset(ac2).subtractOffset(ac2);
200             Assertions.assertEquals(0.0, FieldRotation.distance(ac1.getRotation(), roundTripAS.getRotation()).getReal(), 6.0e-16);
201             Assertions.assertEquals(0.0, FieldVector3D.distance(ac1.getRotationRate(), roundTripAS.getRotationRate()).getReal(), 2.0e-17);
202             Assertions.assertEquals(0.0, FieldVector3D.distance(ac1.getRotationAcceleration(), roundTripAS.getRotationAcceleration()).getReal(), 2.0e-17);
203 
204         }
205     }
206 
207     @Test
208     public void testDerivativesStructures0() {
209         RandomGenerator random = new Well1024a(0x18a0a08fd63f047al);
210 
211         FieldRotation<Binary64> r    = randomRotation64(random);
212         FieldVector3D<Binary64> o    = randomVector64(random, 1.0e-2);
213         FieldVector3D<Binary64> oDot = randomVector64(random, 1.0e-2);
214         TimeStampedFieldAngularCoordinates<Binary64> ac =
215                         new TimeStampedFieldAngularCoordinates<>(FieldAbsoluteDate.getGalileoEpoch(Binary64Field.getInstance()),
216                                                                  r, o, oDot);
217         TimeStampedFieldAngularCoordinates<Binary64> rebuilt =
218                         new TimeStampedFieldAngularCoordinates<>(FieldAbsoluteDate.getGalileoEpoch(Binary64Field.getInstance()),
219                                                                  ac.toDerivativeStructureRotation(0));
220         Assertions.assertEquals(0.0, FieldRotation.distance(ac.getRotation(), rebuilt.getRotation()).getReal(), 1.0e-15);
221         Assertions.assertEquals(0.0, rebuilt.getRotationRate().getNorm().getReal(), 1.0e-15);
222         Assertions.assertEquals(0.0, rebuilt.getRotationAcceleration().getNorm().getReal(), 1.0e-15);
223     }
224 
225     @Test
226     public void testDerivativesStructures1() {
227         RandomGenerator random = new Well1024a(0x8f8fc6d27bbdc46dl);
228 
229         FieldRotation<Binary64> r    = randomRotation64(random);
230         FieldVector3D<Binary64> o    = randomVector64(random, 1.0e-2);
231         FieldVector3D<Binary64> oDot = randomVector64(random, 1.0e-2);
232         TimeStampedFieldAngularCoordinates<Binary64> ac =
233                         new TimeStampedFieldAngularCoordinates<>(FieldAbsoluteDate.getGalileoEpoch(Binary64Field.getInstance()),
234                                                                  r, o, oDot);
235         TimeStampedFieldAngularCoordinates<Binary64> rebuilt =
236                         new TimeStampedFieldAngularCoordinates<>(FieldAbsoluteDate.getGalileoEpoch(Binary64Field.getInstance()),
237                                                                  ac.toDerivativeStructureRotation(1));
238         Assertions.assertEquals(0.0, FieldRotation.distance(ac.getRotation(), rebuilt.getRotation()).getReal(), 1.0e-15);
239         Assertions.assertEquals(0.0, FieldVector3D.distance(ac.getRotationRate(), rebuilt.getRotationRate()).getReal(), 1.0e-15);
240         Assertions.assertEquals(0.0, rebuilt.getRotationAcceleration().getNorm().getReal(), 1.0e-15);
241     }
242 
243     @Test
244     public void testDerivativesStructures2() {
245         RandomGenerator random = new Well1024a(0x1633878dddac047dl);
246 
247         FieldRotation<Binary64> r    = randomRotation64(random);
248         FieldVector3D<Binary64> o    = randomVector64(random, 1.0e-2);
249         FieldVector3D<Binary64> oDot = randomVector64(random, 1.0e-2);
250         TimeStampedFieldAngularCoordinates<Binary64> ac =
251                         new TimeStampedFieldAngularCoordinates<>(FieldAbsoluteDate.getGalileoEpoch(Binary64Field.getInstance()),
252                                                                  r, o, oDot);
253         TimeStampedFieldAngularCoordinates<Binary64> rebuilt =
254                         new TimeStampedFieldAngularCoordinates<>(FieldAbsoluteDate.getGalileoEpoch(Binary64Field.getInstance()),
255                                                                  ac.toDerivativeStructureRotation(2));
256         Assertions.assertEquals(0.0, FieldRotation.distance(ac.getRotation(), rebuilt.getRotation()).getReal(), 1.0e-15);
257         Assertions.assertEquals(0.0, FieldVector3D.distance(ac.getRotationRate(), rebuilt.getRotationRate()).getReal(), 1.0e-15);
258         Assertions.assertEquals(0.0, FieldVector3D.distance(ac.getRotationAcceleration(), rebuilt.getRotationAcceleration()).getReal(), 1.0e-15);
259 
260     }
261 
262     @Test
263     public void testUnivariateDerivative1() {
264         RandomGenerator random = new Well1024a(0x6de8cce747539904l);
265 
266         FieldRotation<Binary64> r    = randomRotation64(random);
267         FieldVector3D<Binary64> o    = randomVector64(random, 1.0e-2);
268         FieldVector3D<Binary64> oDot = randomVector64(random, 1.0e-2);
269         TimeStampedFieldAngularCoordinates<Binary64> ac =
270                         new TimeStampedFieldAngularCoordinates<>(FieldAbsoluteDate.getGalileoEpoch(Binary64Field.getInstance()),
271                                                                  r, o, oDot);
272         FieldRotation<FieldUnivariateDerivative1<Binary64>> rotationUD = ac.toUnivariateDerivative1Rotation();
273         FieldRotation<FieldDerivativeStructure<Binary64>>   rotationDS = ac.toDerivativeStructureRotation(1);
274         Assertions.assertEquals(rotationDS.getQ0().getReal(), rotationUD.getQ0().getReal(), 1.0e-15);
275         Assertions.assertEquals(rotationDS.getQ1().getReal(), rotationUD.getQ1().getReal(), 1.0e-15);
276         Assertions.assertEquals(rotationDS.getQ2().getReal(), rotationUD.getQ2().getReal(), 1.0e-15);
277         Assertions.assertEquals(rotationDS.getQ3().getReal(), rotationUD.getQ3().getReal(), 1.0e-15);
278         Assertions.assertEquals(rotationDS.getQ0().getPartialDerivative(1).getReal(), rotationUD.getQ0().getFirstDerivative().getReal(), 1.0e-15);
279         Assertions.assertEquals(rotationDS.getQ1().getPartialDerivative(1).getReal(), rotationUD.getQ1().getFirstDerivative().getReal(), 1.0e-15);
280         Assertions.assertEquals(rotationDS.getQ2().getPartialDerivative(1).getReal(), rotationUD.getQ2().getFirstDerivative().getReal(), 1.0e-15);
281         Assertions.assertEquals(rotationDS.getQ3().getPartialDerivative(1).getReal(), rotationUD.getQ3().getFirstDerivative().getReal(), 1.0e-15);
282 
283         TimeStampedFieldAngularCoordinates<Binary64> rebuilt =
284                         new TimeStampedFieldAngularCoordinates<>(FieldAbsoluteDate.getGalileoEpoch(Binary64Field.getInstance()),
285                                                                  rotationUD);
286         Assertions.assertEquals(0.0, FieldRotation.distance(ac.getRotation(), rebuilt.getRotation()).getReal(), 1.0e-15);
287         Assertions.assertEquals(0.0, FieldVector3D.distance(ac.getRotationRate(), rebuilt.getRotationRate()).getReal(), 1.0e-15);
288 
289     }
290 
291     @Test
292     public void testUnivariateDerivative2() {
293         RandomGenerator random = new Well1024a(0x255710c8fa2247ecl);
294 
295         FieldRotation<Binary64> r    = randomRotation64(random);
296         FieldVector3D<Binary64> o    = randomVector64(random, 1.0e-2);
297         FieldVector3D<Binary64> oDot = randomVector64(random, 1.0e-2);
298         TimeStampedFieldAngularCoordinates<Binary64> ac =
299                         new TimeStampedFieldAngularCoordinates<>(FieldAbsoluteDate.getGalileoEpoch(Binary64Field.getInstance()),
300                                                                  r, o, oDot);
301         FieldRotation<FieldUnivariateDerivative2<Binary64>> rotationUD = ac.toUnivariateDerivative2Rotation();
302         FieldRotation<FieldDerivativeStructure<Binary64>>   rotationDS = ac.toDerivativeStructureRotation(2);
303         Assertions.assertEquals(rotationDS.getQ0().getReal(), rotationUD.getQ0().getReal(), 1.0e-15);
304         Assertions.assertEquals(rotationDS.getQ1().getReal(), rotationUD.getQ1().getReal(), 1.0e-15);
305         Assertions.assertEquals(rotationDS.getQ2().getReal(), rotationUD.getQ2().getReal(), 1.0e-15);
306         Assertions.assertEquals(rotationDS.getQ3().getReal(), rotationUD.getQ3().getReal(), 1.0e-15);
307         Assertions.assertEquals(rotationDS.getQ0().getPartialDerivative(1).getReal(), rotationUD.getQ0().getFirstDerivative().getReal(), 1.0e-15);
308         Assertions.assertEquals(rotationDS.getQ1().getPartialDerivative(1).getReal(), rotationUD.getQ1().getFirstDerivative().getReal(), 1.0e-15);
309         Assertions.assertEquals(rotationDS.getQ2().getPartialDerivative(1).getReal(), rotationUD.getQ2().getFirstDerivative().getReal(), 1.0e-15);
310         Assertions.assertEquals(rotationDS.getQ3().getPartialDerivative(1).getReal(), rotationUD.getQ3().getFirstDerivative().getReal(), 1.0e-15);
311         Assertions.assertEquals(rotationDS.getQ0().getPartialDerivative(2).getReal(), rotationUD.getQ0().getSecondDerivative().getReal(), 1.0e-15);
312         Assertions.assertEquals(rotationDS.getQ1().getPartialDerivative(2).getReal(), rotationUD.getQ1().getSecondDerivative().getReal(), 1.0e-15);
313         Assertions.assertEquals(rotationDS.getQ2().getPartialDerivative(2).getReal(), rotationUD.getQ2().getSecondDerivative().getReal(), 1.0e-15);
314         Assertions.assertEquals(rotationDS.getQ3().getPartialDerivative(2).getReal(), rotationUD.getQ3().getSecondDerivative().getReal(), 1.0e-15);
315 
316         TimeStampedFieldAngularCoordinates<Binary64> rebuilt =
317                         new TimeStampedFieldAngularCoordinates<>(FieldAbsoluteDate.getGalileoEpoch(Binary64Field.getInstance()),
318                                                                  rotationUD);
319         Assertions.assertEquals(0.0, FieldRotation.distance(ac.getRotation(), rebuilt.getRotation()).getReal(), 1.0e-15);
320         Assertions.assertEquals(0.0, FieldVector3D.distance(ac.getRotationRate(), rebuilt.getRotationRate()).getReal(), 1.0e-15);
321         Assertions.assertEquals(0.0, FieldVector3D.distance(ac.getRotationAcceleration(), rebuilt.getRotationAcceleration()).getReal(), 1.0e-15);
322 
323     }
324 
325     @Test
326     public void testIssue773() {
327         doTestIssue773(Binary64Field.getInstance());
328     }
329 
330     private <T extends CalculusFieldElement<T>> void doTestIssue773(final Field<T> field) {
331         // Epoch
332         final AbsoluteDate date = new AbsoluteDate();
333 
334         // Coordinates
335         final TimeStampedAngularCoordinates angular =
336                         new TimeStampedAngularCoordinates(date,
337                                                           new Rotation(0., 0., 0., 0., false),
338                                                           Vector3D.ZERO,
339                                                           Vector3D.ZERO);
340 
341         // Time stamped object
342         final FieldTimeStamped<T> timeStamped =
343                         new TimeStampedFieldAngularCoordinates<>(field, angular);
344 
345         // Verify
346         Assertions.assertEquals(0.0, date.durationFrom(timeStamped.getDate().toAbsoluteDate()), Double.MIN_VALUE);
347     }
348 
349     private FieldVector3D<DerivativeStructure> randomVector(Random random, double norm) {
350         double n = random.nextDouble() * norm;
351         double x = random.nextDouble();
352         double y = random.nextDouble();
353         double z = random.nextDouble();
354         return new FieldVector3D<>(n, createVector(x, y, z, 4).normalize());
355     }
356 
357     private FieldRotation<DerivativeStructure> randomRotation(Random random) {
358         double q0 = random.nextDouble() * 2 - 1;
359         double q1 = random.nextDouble() * 2 - 1;
360         double q2 = random.nextDouble() * 2 - 1;
361         double q3 = random.nextDouble() * 2 - 1;
362         double q  = FastMath.sqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
363         return createRotation(q0 / q, q1 / q, q2 / q, q3 / q, false);
364     }
365 
366     public static FieldRotation<DerivativeStructure> createRotation(FieldVector3D<DerivativeStructure> axis, double angle) {
367         return new FieldRotation<>(axis,
368                                    new DSFactory(4, 1).constant(angle),
369                                    RotationConvention.VECTOR_OPERATOR);
370     }
371 
372     public static FieldRotation<DerivativeStructure> createRotation(double q0, double q1, double q2, double q3,
373                                                                     boolean needsNormalization) {
374         DSFactory factory = new DSFactory(4, 1);
375         return new FieldRotation<>(factory.variable(0, q0),
376                                    factory.variable(1, q1),
377                                    factory.variable(2, q2),
378                                    factory.variable(3, q3),
379                                    needsNormalization);
380     }
381 
382     public static FieldVector3D<DerivativeStructure> createVector(double x, double y, double z, int params) {
383         DSFactory factory = new DSFactory(params, 1);
384         return new FieldVector3D<>(factory.variable(0, x),
385                                    factory.variable(1, y),
386                                    factory.variable(2, z));
387     }
388 
389     private FieldRotation<Binary64> randomRotation64(RandomGenerator random) {
390         double q0 = random.nextDouble() * 2 - 1;
391         double q1 = random.nextDouble() * 2 - 1;
392         double q2 = random.nextDouble() * 2 - 1;
393         double q3 = random.nextDouble() * 2 - 1;
394         double q  = FastMath.sqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
395         return new FieldRotation<>(new Binary64(q0 / q),
396                                    new Binary64(q1 / q),
397                                    new Binary64(q2 / q),
398                                    new Binary64(q3 / q),
399                                    false);
400     }
401 
402     private FieldVector3D<Binary64> randomVector64(RandomGenerator random, double norm) {
403         double n = random.nextDouble() * norm;
404         double x = random.nextDouble();
405         double y = random.nextDouble();
406         double z = random.nextDouble();
407         return new FieldVector3D<>(n, new FieldVector3D<>(new Binary64(x), new Binary64(y), new Binary64(z)).normalize());
408     }
409 
410     @BeforeEach
411     public void setUp() {
412         Utils.setDataRoot("regular-data");
413     }
414 
415 }
416