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