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17 package org.orekit.orbits;
18
19
20 import java.lang.reflect.Array;
21
22 import org.hipparchus.CalculusFieldElement;
23 import org.hipparchus.Field;
24 import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative1;
25 import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
26 import org.hipparchus.util.FastMath;
27 import org.hipparchus.util.FieldSinCos;
28 import org.hipparchus.util.MathArrays;
29 import org.orekit.errors.OrekitException;
30 import org.orekit.errors.OrekitIllegalArgumentException;
31 import org.orekit.errors.OrekitInternalError;
32 import org.orekit.errors.OrekitMessages;
33 import org.orekit.frames.FieldKinematicTransform;
34 import org.orekit.frames.Frame;
35 import org.orekit.time.FieldAbsoluteDate;
36 import org.orekit.utils.FieldPVCoordinates;
37 import org.orekit.utils.TimeStampedFieldPVCoordinates;
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81 public class FieldKeplerianOrbit<T extends CalculusFieldElement<T>> extends FieldOrbit<T>
82 implements PositionAngleBased<FieldKeplerianOrbit<T>> {
83
84
85 private static final String ECCENTRICITY = "eccentricity";
86
87
88 private final T a;
89
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91 private final T e;
92
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94 private final T i;
95
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97 private final T pa;
98
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100 private final T raan;
101
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103 private final T cachedAnomaly;
104
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106 private final T aDot;
107
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109 private final T eDot;
110
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112 private final T iDot;
113
114
115 private final T paDot;
116
117
118 private final T raanDot;
119
120
121 private final T cachedAnomalyDot;
122
123
124 private final PositionAngleType cachedPositionAngleType;
125
126
127 private FieldPVCoordinates<T> partialPV;
128
129
130 private final FieldVector3D<T> PLUS_K;
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150 public FieldKeplerianOrbit(final T a, final T e, final T i,
151 final T pa, final T raan,
152 final T anomaly, final PositionAngleType type,
153 final PositionAngleType cachedPositionAngleType,
154 final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
155 throws IllegalArgumentException {
156 this(a, e, i, pa, raan, anomaly,
157 a.getField().getZero(), a.getField().getZero(), a.getField().getZero(), a.getField().getZero(), a.getField().getZero(),
158 computeKeplerianAnomalyDot(type, a, e, mu, anomaly, type), type, cachedPositionAngleType, frame, date, mu);
159 }
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178 public FieldKeplerianOrbit(final T a, final T e, final T i,
179 final T pa, final T raan,
180 final T anomaly, final PositionAngleType type,
181 final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
182 throws IllegalArgumentException {
183 this(a, e, i, pa, raan, anomaly, type, type, frame, date, mu);
184 }
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210 public FieldKeplerianOrbit(final T a, final T e, final T i,
211 final T pa, final T raan, final T anomaly,
212 final T aDot, final T eDot, final T iDot,
213 final T paDot, final T raanDot, final T anomalyDot,
214 final PositionAngleType type, final PositionAngleType cachedPositionAngleType,
215 final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
216 throws IllegalArgumentException {
217 super(frame, date, mu);
218 this.cachedPositionAngleType = cachedPositionAngleType;
219
220 if (a.multiply(e.negate().add(1)).getReal() < 0) {
221 throw new OrekitIllegalArgumentException(OrekitMessages.ORBIT_A_E_MISMATCH_WITH_CONIC_TYPE, a.getReal(), e.getReal());
222 }
223
224
225 checkParameterRangeInclusive(ECCENTRICITY, e.getReal(), 0.0, Double.POSITIVE_INFINITY);
226
227 this.a = a;
228 this.aDot = aDot;
229 this.e = e;
230 this.eDot = eDot;
231 this.i = i;
232 this.iDot = iDot;
233 this.pa = pa;
234 this.paDot = paDot;
235 this.raan = raan;
236 this.raanDot = raanDot;
237
238 this.PLUS_K = FieldVector3D.getPlusK(a.getField());
239
240 final FieldUnivariateDerivative1<T> cachedAnomalyUD = initializeCachedAnomaly(anomaly, anomalyDot, type);
241 this.cachedAnomaly = cachedAnomalyUD.getValue();
242 this.cachedAnomalyDot = cachedAnomalyUD.getFirstDerivative();
243
244
245 if (!isElliptical()) {
246 final T trueAnomaly = getTrueAnomaly();
247 if (e.multiply(trueAnomaly.cos()).add(1).getReal() <= 0) {
248 final double vMax = e.reciprocal().negate().acos().getReal();
249 throw new OrekitIllegalArgumentException(OrekitMessages.ORBIT_ANOMALY_OUT_OF_HYPERBOLIC_RANGE,
250 trueAnomaly.getReal(), e.getReal(), -vMax, vMax);
251 }
252 }
253
254 this.partialPV = null;
255
256 }
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280 public FieldKeplerianOrbit(final T a, final T e, final T i,
281 final T pa, final T raan, final T anomaly,
282 final T aDot, final T eDot, final T iDot,
283 final T paDot, final T raanDot, final T anomalyDot,
284 final PositionAngleType type,
285 final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
286 throws IllegalArgumentException {
287 this(a, e, i, pa, raan, anomaly, aDot, eDot, iDot, paDot, raanDot, anomalyDot,
288 type, type, frame, date, mu);
289 }
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305 public FieldKeplerianOrbit(final TimeStampedFieldPVCoordinates<T> pvCoordinates,
306 final Frame frame, final T mu)
307 throws IllegalArgumentException {
308 this(pvCoordinates, frame, mu, hasNonKeplerianAcceleration(pvCoordinates, mu));
309 }
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326 private FieldKeplerianOrbit(final TimeStampedFieldPVCoordinates<T> pvCoordinates,
327 final Frame frame, final T mu,
328 final boolean reliableAcceleration)
329 throws IllegalArgumentException {
330
331 super(pvCoordinates, frame, mu);
332
333
334 this.PLUS_K = FieldVector3D.getPlusK(getOne().getField());
335
336
337 final FieldVector3D<T> momentum = pvCoordinates.getMomentum();
338 final T m2 = momentum.getNormSq();
339
340 i = FieldVector3D.angle(momentum, PLUS_K);
341
342 raan = FieldVector3D.crossProduct(PLUS_K, momentum).getAlpha();
343
344 final FieldVector3D<T> pvP = pvCoordinates.getPosition();
345 final FieldVector3D<T> pvV = pvCoordinates.getVelocity();
346 final FieldVector3D<T> pvA = pvCoordinates.getAcceleration();
347
348 final T r2 = pvP.getNormSq();
349 final T r = r2.sqrt();
350 final T V2 = pvV.getNormSq();
351 final T rV2OnMu = r.multiply(V2).divide(mu);
352
353
354 a = r.divide(rV2OnMu.negate().add(2.0));
355 final T muA = a.multiply(mu);
356
357
358 if (isElliptical()) {
359
360 final T eSE = FieldVector3D.dotProduct(pvP, pvV).divide(muA.sqrt());
361 final T eCE = rV2OnMu.subtract(1);
362 e = (eSE.multiply(eSE).add(eCE.multiply(eCE))).sqrt();
363 this.cachedPositionAngleType = PositionAngleType.ECCENTRIC;
364 cachedAnomaly = eSE.atan2(eCE);
365 } else {
366
367 final T eSH = FieldVector3D.dotProduct(pvP, pvV).divide(muA.negate().sqrt());
368 final T eCH = rV2OnMu.subtract(1);
369 e = (m2.negate().divide(muA).add(1)).sqrt();
370 this.cachedPositionAngleType = PositionAngleType.TRUE;
371 cachedAnomaly = FieldKeplerianAnomalyUtility.hyperbolicEccentricToTrue(e, (eCH.add(eSH)).divide(eCH.subtract(eSH)).log().divide(2));
372 }
373
374
375 checkParameterRangeInclusive(ECCENTRICITY, e.getReal(), 0.0, Double.POSITIVE_INFINITY);
376
377
378 final FieldVector3D<T> node = new FieldVector3D<>(raan, getZero());
379 final T px = FieldVector3D.dotProduct(pvP, node);
380 final T py = FieldVector3D.dotProduct(pvP, FieldVector3D.crossProduct(momentum, node)).divide(m2.sqrt());
381 pa = py.atan2(px).subtract(getTrueAnomaly());
382
383 partialPV = pvCoordinates;
384
385 if (reliableAcceleration) {
386
387
388 final T[][] jacobian = MathArrays.buildArray(a.getField(), 6, 6);
389 getJacobianWrtCartesian(PositionAngleType.MEAN, jacobian);
390
391 final FieldVector3D<T> keplerianAcceleration = new FieldVector3D<>(r.multiply(r2).reciprocal().multiply(mu.negate()), pvP);
392 final FieldVector3D<T> nonKeplerianAcceleration = pvA.subtract(keplerianAcceleration);
393 final T aX = nonKeplerianAcceleration.getX();
394 final T aY = nonKeplerianAcceleration.getY();
395 final T aZ = nonKeplerianAcceleration.getZ();
396 aDot = jacobian[0][3].multiply(aX).add(jacobian[0][4].multiply(aY)).add(jacobian[0][5].multiply(aZ));
397 eDot = jacobian[1][3].multiply(aX).add(jacobian[1][4].multiply(aY)).add(jacobian[1][5].multiply(aZ));
398 iDot = jacobian[2][3].multiply(aX).add(jacobian[2][4].multiply(aY)).add(jacobian[2][5].multiply(aZ));
399 paDot = jacobian[3][3].multiply(aX).add(jacobian[3][4].multiply(aY)).add(jacobian[3][5].multiply(aZ));
400 raanDot = jacobian[4][3].multiply(aX).add(jacobian[4][4].multiply(aY)).add(jacobian[4][5].multiply(aZ));
401
402
403
404 final T MDot = getKeplerianMeanMotion().
405 add(jacobian[5][3].multiply(aX)).add(jacobian[5][4].multiply(aY)).add(jacobian[5][5].multiply(aZ));
406 final FieldUnivariateDerivative1<T> eUD = new FieldUnivariateDerivative1<>(e, eDot);
407 final FieldUnivariateDerivative1<T> MUD = new FieldUnivariateDerivative1<>(getMeanAnomaly(), MDot);
408 if (cachedPositionAngleType == PositionAngleType.ECCENTRIC) {
409 final FieldUnivariateDerivative1<T> EUD = (a.getReal() < 0) ?
410 FieldKeplerianAnomalyUtility.hyperbolicMeanToEccentric(eUD, MUD) :
411 FieldKeplerianAnomalyUtility.ellipticMeanToEccentric(eUD, MUD);
412 cachedAnomalyDot = EUD.getFirstDerivative();
413 } else {
414 final FieldUnivariateDerivative1<T> vUD = (a.getReal() < 0) ?
415 FieldKeplerianAnomalyUtility.hyperbolicMeanToTrue(eUD, MUD) :
416 FieldKeplerianAnomalyUtility.ellipticMeanToTrue(eUD, MUD);
417 cachedAnomalyDot = vUD.getFirstDerivative();
418 }
419
420 } else {
421
422
423
424 aDot = getZero();
425 eDot = getZero();
426 iDot = getZero();
427 paDot = getZero();
428 raanDot = getZero();
429 cachedAnomalyDot = computeKeplerianAnomalyDot(cachedPositionAngleType, a, e, mu, cachedAnomaly, cachedPositionAngleType);
430 }
431
432 }
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449 public FieldKeplerianOrbit(final FieldPVCoordinates<T> FieldPVCoordinates,
450 final Frame frame, final FieldAbsoluteDate<T> date, final T mu)
451 throws IllegalArgumentException {
452 this(new TimeStampedFieldPVCoordinates<>(date, FieldPVCoordinates), frame, mu);
453 }
454
455
456
457
458 public FieldKeplerianOrbit(final FieldOrbit<T> op) {
459 this(op.getPVCoordinates(), op.getFrame(), op.getMu());
460 }
461
462
463
464
465
466
467
468 public FieldKeplerianOrbit(final Field<T> field, final KeplerianOrbit op) {
469 this(field.getZero().newInstance(op.getA()), field.getZero().newInstance(op.getE()), field.getZero().newInstance(op.getI()),
470 field.getZero().newInstance(op.getPerigeeArgument()), field.getZero().newInstance(op.getRightAscensionOfAscendingNode()),
471 field.getZero().newInstance(op.getAnomaly(op.getCachedPositionAngleType())),
472 field.getZero().newInstance(op.getADot()),
473 field.getZero().newInstance(op.getEDot()),
474 field.getZero().newInstance(op.getIDot()),
475 field.getZero().newInstance(op.getPerigeeArgumentDot()),
476 field.getZero().newInstance(op.getRightAscensionOfAscendingNodeDot()),
477 field.getZero().newInstance(op.getAnomalyDot(op.getCachedPositionAngleType())),
478 op.getCachedPositionAngleType(), op.getFrame(),
479 new FieldAbsoluteDate<>(field, op.getDate()), field.getZero().newInstance(op.getMu()));
480 }
481
482
483
484
485
486
487
488 public FieldKeplerianOrbit(final Field<T> field, final Orbit op) {
489 this(field, (KeplerianOrbit) OrbitType.KEPLERIAN.convertType(op));
490 }
491
492
493 @Override
494 public OrbitType getType() {
495 return OrbitType.KEPLERIAN;
496 }
497
498
499 @Override
500 public T getA() {
501 return a;
502 }
503
504
505 @Override
506 public T getADot() {
507 return aDot;
508 }
509
510
511 @Override
512 public T getE() {
513 return e;
514 }
515
516
517 @Override
518 public T getEDot() {
519 return eDot;
520 }
521
522
523 @Override
524 public T getI() {
525 return i;
526 }
527
528
529 @Override
530 public T getIDot() {
531 return iDot;
532 }
533
534
535
536
537 public T getPerigeeArgument() {
538 return pa;
539 }
540
541
542
543
544 public T getPerigeeArgumentDot() {
545 return paDot;
546 }
547
548
549
550
551 public T getRightAscensionOfAscendingNode() {
552 return raan;
553 }
554
555
556
557
558 public T getRightAscensionOfAscendingNodeDot() {
559 return raanDot;
560 }
561
562
563
564
565 public T getTrueAnomaly() {
566 switch (cachedPositionAngleType) {
567 case MEAN: return (a.getReal() < 0) ? FieldKeplerianAnomalyUtility.hyperbolicMeanToTrue(e, cachedAnomaly) :
568 FieldKeplerianAnomalyUtility.ellipticMeanToTrue(e, cachedAnomaly);
569
570 case TRUE: return cachedAnomaly;
571
572 case ECCENTRIC: return (a.getReal() < 0) ? FieldKeplerianAnomalyUtility.hyperbolicEccentricToTrue(e, cachedAnomaly) :
573 FieldKeplerianAnomalyUtility.ellipticEccentricToTrue(e, cachedAnomaly);
574
575 default: throw new OrekitInternalError(null);
576 }
577 }
578
579
580
581
582 public T getTrueAnomalyDot() {
583 switch (cachedPositionAngleType) {
584 case MEAN:
585 final FieldUnivariateDerivative1<T> eUD = new FieldUnivariateDerivative1<>(e, eDot);
586 final FieldUnivariateDerivative1<T> MUD = new FieldUnivariateDerivative1<>(cachedAnomaly, cachedAnomalyDot);
587 final FieldUnivariateDerivative1<T> vUD = (a.getReal() < 0) ?
588 FieldKeplerianAnomalyUtility.hyperbolicMeanToTrue(eUD, MUD) :
589 FieldKeplerianAnomalyUtility.ellipticMeanToTrue(eUD, MUD);
590 return vUD.getFirstDerivative();
591
592 case TRUE:
593 return cachedAnomalyDot;
594
595 case ECCENTRIC:
596 final FieldUnivariateDerivative1<T> eUD2 = new FieldUnivariateDerivative1<>(e, eDot);
597 final FieldUnivariateDerivative1<T> EUD = new FieldUnivariateDerivative1<>(cachedAnomaly, cachedAnomalyDot);
598 final FieldUnivariateDerivative1<T> vUD2 = (a.getReal() < 0) ?
599 FieldKeplerianAnomalyUtility.hyperbolicEccentricToTrue(eUD2, EUD) :
600 FieldKeplerianAnomalyUtility.ellipticEccentricToTrue(eUD2, EUD);
601 return vUD2.getFirstDerivative();
602
603 default:
604 throw new OrekitInternalError(null);
605 }
606 }
607
608
609
610
611 public T getEccentricAnomaly() {
612 switch (cachedPositionAngleType) {
613 case MEAN:
614 return (a.getReal() < 0) ? FieldKeplerianAnomalyUtility.hyperbolicMeanToEccentric(e, cachedAnomaly) :
615 FieldKeplerianAnomalyUtility.ellipticMeanToEccentric(e, cachedAnomaly);
616
617 case ECCENTRIC:
618 return cachedAnomaly;
619
620 case TRUE:
621 return (a.getReal() < 0) ? FieldKeplerianAnomalyUtility.hyperbolicTrueToEccentric(e, cachedAnomaly) :
622 FieldKeplerianAnomalyUtility.ellipticTrueToEccentric(e, cachedAnomaly);
623
624 default:
625 throw new OrekitInternalError(null);
626 }
627 }
628
629
630
631
632 public T getEccentricAnomalyDot() {
633 switch (cachedPositionAngleType) {
634 case ECCENTRIC:
635 return cachedAnomalyDot;
636
637 case TRUE:
638 final FieldUnivariateDerivative1<T> eUD = new FieldUnivariateDerivative1<>(e, eDot);
639 final FieldUnivariateDerivative1<T> vUD = new FieldUnivariateDerivative1<>(cachedAnomaly, cachedAnomalyDot);
640 final FieldUnivariateDerivative1<T> EUD = (a.getReal() < 0) ?
641 FieldKeplerianAnomalyUtility.hyperbolicTrueToEccentric(eUD, vUD) :
642 FieldKeplerianAnomalyUtility.ellipticTrueToEccentric(eUD, vUD);
643 return EUD.getFirstDerivative();
644
645 case MEAN:
646 final FieldUnivariateDerivative1<T> eUD2 = new FieldUnivariateDerivative1<>(e, eDot);
647 final FieldUnivariateDerivative1<T> MUD = new FieldUnivariateDerivative1<>(cachedAnomaly, cachedAnomalyDot);
648 final FieldUnivariateDerivative1<T> EUD2 = (a.getReal() < 0) ?
649 FieldKeplerianAnomalyUtility.hyperbolicMeanToEccentric(eUD2, MUD) :
650 FieldKeplerianAnomalyUtility.ellipticMeanToEccentric(eUD2, MUD);
651 return EUD2.getFirstDerivative();
652
653 default:
654 throw new OrekitInternalError(null);
655 }
656 }
657
658
659
660
661 public T getMeanAnomaly() {
662 switch (cachedPositionAngleType) {
663 case ECCENTRIC: return (a.getReal() < 0) ? FieldKeplerianAnomalyUtility.hyperbolicEccentricToMean(e, cachedAnomaly) :
664 FieldKeplerianAnomalyUtility.ellipticEccentricToMean(e, cachedAnomaly);
665
666 case MEAN: return cachedAnomaly;
667
668 case TRUE: return (a.getReal() < 0) ? FieldKeplerianAnomalyUtility.hyperbolicTrueToMean(e, cachedAnomaly) :
669 FieldKeplerianAnomalyUtility.ellipticTrueToMean(e, cachedAnomaly);
670
671 default: throw new OrekitInternalError(null);
672 }
673 }
674
675
676
677
678
679 public T getMeanAnomalyDot() {
680 switch (cachedPositionAngleType) {
681 case MEAN:
682 return cachedAnomalyDot;
683
684 case ECCENTRIC:
685 final FieldUnivariateDerivative1<T> eUD = new FieldUnivariateDerivative1<>(e, eDot);
686 final FieldUnivariateDerivative1<T> EUD = new FieldUnivariateDerivative1<>(cachedAnomaly, cachedAnomalyDot);
687 final FieldUnivariateDerivative1<T> MUD = (a.getReal() < 0) ?
688 FieldKeplerianAnomalyUtility.hyperbolicEccentricToMean(eUD, EUD) :
689 FieldKeplerianAnomalyUtility.ellipticEccentricToMean(eUD, EUD);
690 return MUD.getFirstDerivative();
691
692 case TRUE:
693 final FieldUnivariateDerivative1<T> eUD2 = new FieldUnivariateDerivative1<>(e, eDot);
694 final FieldUnivariateDerivative1<T> vUD = new FieldUnivariateDerivative1<>(cachedAnomaly, cachedAnomalyDot);
695 final FieldUnivariateDerivative1<T> MUD2 = (a.getReal() < 0) ?
696 FieldKeplerianAnomalyUtility.hyperbolicTrueToMean(eUD2, vUD) :
697 FieldKeplerianAnomalyUtility.ellipticTrueToMean(eUD2, vUD);
698 return MUD2.getFirstDerivative();
699
700 default:
701 throw new OrekitInternalError(null);
702 }
703 }
704
705
706
707
708
709 public T getAnomaly(final PositionAngleType type) {
710 return (type == PositionAngleType.MEAN) ? getMeanAnomaly() :
711 ((type == PositionAngleType.ECCENTRIC) ? getEccentricAnomaly() :
712 getTrueAnomaly());
713 }
714
715
716
717
718
719 public T getAnomalyDot(final PositionAngleType type) {
720 return (type == PositionAngleType.MEAN) ? getMeanAnomalyDot() :
721 ((type == PositionAngleType.ECCENTRIC) ? getEccentricAnomalyDot() :
722 getTrueAnomalyDot());
723 }
724
725
726 @Override
727 public boolean hasNonKeplerianAcceleration() {
728 return aDot.getReal() != 0. || eDot.getReal() != 0 || iDot.getReal() != 0. || raanDot.getReal() != 0. || paDot.getReal() != 0. ||
729 FastMath.abs(cachedAnomalyDot.subtract(computeKeplerianAnomalyDot(cachedPositionAngleType, a, e, getMu(), cachedAnomaly, cachedPositionAngleType)).getReal()) > TOLERANCE_POSITION_ANGLE_RATE;
730 }
731
732
733 @Override
734 public T getEquinoctialEx() {
735 return e.multiply(pa.add(raan).cos());
736 }
737
738
739 @Override
740 public T getEquinoctialExDot() {
741 if (!hasNonKeplerianRates()) {
742 return getZero();
743 }
744 final FieldUnivariateDerivative1<T> eUD = new FieldUnivariateDerivative1<>(e, eDot);
745 final FieldUnivariateDerivative1<T> paUD = new FieldUnivariateDerivative1<>(pa, paDot);
746 final FieldUnivariateDerivative1<T> raanUD = new FieldUnivariateDerivative1<>(raan, raanDot);
747 return eUD.multiply(paUD.add(raanUD).cos()).getFirstDerivative();
748
749 }
750
751
752 @Override
753 public T getEquinoctialEy() {
754 return e.multiply((pa.add(raan)).sin());
755 }
756
757
758 @Override
759 public T getEquinoctialEyDot() {
760 if (!hasNonKeplerianRates()) {
761 return getZero();
762 }
763 final FieldUnivariateDerivative1<T> eUD = new FieldUnivariateDerivative1<>(e, eDot);
764 final FieldUnivariateDerivative1<T> paUD = new FieldUnivariateDerivative1<>(pa, paDot);
765 final FieldUnivariateDerivative1<T> raanUD = new FieldUnivariateDerivative1<>(raan, raanDot);
766 return eUD.multiply(paUD.add(raanUD).sin()).getFirstDerivative();
767
768 }
769
770
771 @Override
772 public T getHx() {
773
774 if (FastMath.abs(i.subtract(i.getPi()).getReal()) < 1.0e-10) {
775 return getZero().add(Double.NaN);
776 }
777 return raan.cos().multiply(i.divide(2).tan());
778 }
779
780
781 @Override
782 public T getHxDot() {
783
784
785 if (FastMath.abs(i.subtract(i.getPi()).getReal()) < 1.0e-10) {
786 return getZero().add(Double.NaN);
787 }
788 if (!hasNonKeplerianRates()) {
789 return getZero();
790 }
791
792 final FieldUnivariateDerivative1<T> iUD = new FieldUnivariateDerivative1<>(i, iDot);
793 final FieldUnivariateDerivative1<T> raanUD = new FieldUnivariateDerivative1<>(raan, raanDot);
794 return raanUD.cos().multiply(iUD.multiply(0.5).tan()).getFirstDerivative();
795
796 }
797
798
799 @Override
800 public T getHy() {
801
802 if (FastMath.abs(i.subtract(i.getPi()).getReal()) < 1.0e-10) {
803 return getZero().add(Double.NaN);
804 }
805 return raan.sin().multiply(i.divide(2).tan());
806 }
807
808
809 @Override
810 public T getHyDot() {
811
812
813 if (FastMath.abs(i.subtract(i.getPi()).getReal()) < 1.0e-10) {
814 return getZero().add(Double.NaN);
815 }
816 if (!hasNonKeplerianRates()) {
817 return getZero();
818 }
819
820 final FieldUnivariateDerivative1<T> iUD = new FieldUnivariateDerivative1<>(i, iDot);
821 final FieldUnivariateDerivative1<T> raanUD = new FieldUnivariateDerivative1<>(raan, raanDot);
822 return raanUD.sin().multiply(iUD.multiply(0.5).tan()).getFirstDerivative();
823
824 }
825
826
827 @Override
828 public T getLv() {
829 return pa.add(raan).add(getTrueAnomaly());
830 }
831
832
833 @Override
834 public T getLvDot() {
835 return paDot.add(raanDot).add(getTrueAnomalyDot());
836 }
837
838
839 @Override
840 public T getLE() {
841 return pa.add(raan).add(getEccentricAnomaly());
842 }
843
844
845 @Override
846 public T getLEDot() {
847 return paDot.add(raanDot).add(getEccentricAnomalyDot());
848 }
849
850
851 @Override
852 public T getLM() {
853 return pa.add(raan).add(getMeanAnomaly());
854 }
855
856
857 @Override
858 public T getLMDot() {
859 return paDot.add(raanDot).add(getMeanAnomalyDot());
860 }
861
862
863
864
865
866
867
868
869 private FieldUnivariateDerivative1<T> initializeCachedAnomaly(final T anomaly, final T anomalyDot,
870 final PositionAngleType inputType) {
871 if (cachedPositionAngleType == inputType) {
872 return new FieldUnivariateDerivative1<>(anomaly, anomalyDot);
873
874 } else {
875 final FieldUnivariateDerivative1<T> eUD = new FieldUnivariateDerivative1<>(e, eDot);
876 final FieldUnivariateDerivative1<T> anomalyUD = new FieldUnivariateDerivative1<>(anomaly, anomalyDot);
877
878 if (a.getReal() < 0) {
879 switch (cachedPositionAngleType) {
880 case MEAN:
881 if (inputType == PositionAngleType.ECCENTRIC) {
882 return FieldKeplerianAnomalyUtility.hyperbolicEccentricToMean(eUD, anomalyUD);
883 } else {
884 return FieldKeplerianAnomalyUtility.hyperbolicTrueToMean(eUD, anomalyUD);
885 }
886
887 case ECCENTRIC:
888 if (inputType == PositionAngleType.MEAN) {
889 return FieldKeplerianAnomalyUtility.hyperbolicMeanToEccentric(eUD, anomalyUD);
890 } else {
891 return FieldKeplerianAnomalyUtility.hyperbolicTrueToEccentric(eUD, anomalyUD);
892 }
893
894 case TRUE:
895 if (inputType == PositionAngleType.MEAN) {
896 return FieldKeplerianAnomalyUtility.hyperbolicMeanToTrue(eUD, anomalyUD);
897 } else {
898 return FieldKeplerianAnomalyUtility.hyperbolicEccentricToTrue(eUD, anomalyUD);
899 }
900
901 default:
902 break;
903 }
904
905 } else {
906 switch (cachedPositionAngleType) {
907 case MEAN:
908 if (inputType == PositionAngleType.ECCENTRIC) {
909 return FieldKeplerianAnomalyUtility.ellipticEccentricToMean(eUD, anomalyUD);
910 } else {
911 return FieldKeplerianAnomalyUtility.ellipticTrueToMean(eUD, anomalyUD);
912 }
913
914 case ECCENTRIC:
915 if (inputType == PositionAngleType.MEAN) {
916 return FieldKeplerianAnomalyUtility.ellipticMeanToEccentric(eUD, anomalyUD);
917 } else {
918 return FieldKeplerianAnomalyUtility.ellipticTrueToEccentric(eUD, anomalyUD);
919 }
920
921 case TRUE:
922 if (inputType == PositionAngleType.MEAN) {
923 return FieldKeplerianAnomalyUtility.ellipticMeanToTrue(eUD, anomalyUD);
924 } else {
925 return FieldKeplerianAnomalyUtility.ellipticEccentricToTrue(eUD, anomalyUD);
926 }
927
928 default:
929 break;
930 }
931
932 }
933 throw new OrekitInternalError(null);
934 }
935
936 }
937
938
939
940
941
942 private FieldVector3D<T>[] referenceAxes() {
943
944
945 final FieldSinCos<T> scRaan = FastMath.sinCos(raan);
946 final FieldSinCos<T> scPa = FastMath.sinCos(pa);
947 final FieldSinCos<T> scI = FastMath.sinCos(i);
948 final T cosRaan = scRaan.cos();
949 final T sinRaan = scRaan.sin();
950 final T cosPa = scPa.cos();
951 final T sinPa = scPa.sin();
952 final T cosI = scI.cos();
953 final T sinI = scI.sin();
954 final T crcp = cosRaan.multiply(cosPa);
955 final T crsp = cosRaan.multiply(sinPa);
956 final T srcp = sinRaan.multiply(cosPa);
957 final T srsp = sinRaan.multiply(sinPa);
958
959
960 @SuppressWarnings("unchecked")
961 final FieldVector3D<T>[] axes = (FieldVector3D<T>[]) Array.newInstance(FieldVector3D.class, 2);
962 axes[0] = new FieldVector3D<>(crcp.subtract(cosI.multiply(srsp)), srcp.add(cosI.multiply(crsp)), sinI.multiply(sinPa));
963 axes[1] = new FieldVector3D<>(crsp.add(cosI.multiply(srcp)).negate(), cosI.multiply(crcp).subtract(srsp), sinI.multiply(cosPa));
964
965 return axes;
966
967 }
968
969
970
971 private void computePVWithoutA() {
972
973 if (partialPV != null) {
974
975 return;
976 }
977
978 final FieldVector3D<T>[] axes = referenceAxes();
979
980 if (isElliptical()) {
981
982
983
984
985 final T uME2 = e.negate().add(1).multiply(e.add(1));
986 final T s1Me2 = uME2.sqrt();
987 final FieldSinCos<T> scE = FastMath.sinCos(getEccentricAnomaly());
988 final T cosE = scE.cos();
989 final T sinE = scE.sin();
990
991
992 final T x = a.multiply(cosE.subtract(e));
993 final T y = a.multiply(sinE).multiply(s1Me2);
994 final T factor = FastMath.sqrt(getMu().divide(a)).divide(e.negate().multiply(cosE).add(1));
995 final T xDot = sinE.negate().multiply(factor);
996 final T yDot = cosE.multiply(s1Me2).multiply(factor);
997
998 final FieldVector3D<T> position = new FieldVector3D<>(x, axes[0], y, axes[1]);
999 final FieldVector3D<T> velocity = new FieldVector3D<>(xDot, axes[0], yDot, axes[1]);
1000 partialPV = new FieldPVCoordinates<>(position, velocity);
1001
1002 } else {
1003
1004
1005
1006
1007 final FieldSinCos<T> scV = FastMath.sinCos(getTrueAnomaly());
1008 final T sinV = scV.sin();
1009 final T cosV = scV.cos();
1010 final T f = a.multiply(e.square().negate().add(1));
1011 final T posFactor = f.divide(e.multiply(cosV).add(1));
1012 final T velFactor = FastMath.sqrt(getMu().divide(f));
1013
1014 final FieldVector3D<T> position = new FieldVector3D<>(posFactor.multiply(cosV), axes[0], posFactor.multiply(sinV), axes[1]);
1015 final FieldVector3D<T> velocity = new FieldVector3D<>(velFactor.multiply(sinV).negate(), axes[0], velFactor.multiply(e.add(cosV)), axes[1]);
1016 partialPV = new FieldPVCoordinates<>(position, velocity);
1017
1018 }
1019
1020 }
1021
1022
1023
1024
1025 private FieldVector3D<T> nonKeplerianAcceleration() {
1026
1027 final T[][] dCdP = MathArrays.buildArray(a.getField(), 6, 6);
1028 getJacobianWrtParameters(PositionAngleType.MEAN, dCdP);
1029
1030 final T nonKeplerianMeanMotion = getMeanAnomalyDot().subtract(getKeplerianMeanMotion());
1031 final T nonKeplerianAx = dCdP[3][0].multiply(aDot).
1032 add(dCdP[3][1].multiply(eDot)).
1033 add(dCdP[3][2].multiply(iDot)).
1034 add(dCdP[3][3].multiply(paDot)).
1035 add(dCdP[3][4].multiply(raanDot)).
1036 add(dCdP[3][5].multiply(nonKeplerianMeanMotion));
1037 final T nonKeplerianAy = dCdP[4][0].multiply(aDot).
1038 add(dCdP[4][1].multiply(eDot)).
1039 add(dCdP[4][2].multiply(iDot)).
1040 add(dCdP[4][3].multiply(paDot)).
1041 add(dCdP[4][4].multiply(raanDot)).
1042 add(dCdP[4][5].multiply(nonKeplerianMeanMotion));
1043 final T nonKeplerianAz = dCdP[5][0].multiply(aDot).
1044 add(dCdP[5][1].multiply(eDot)).
1045 add(dCdP[5][2].multiply(iDot)).
1046 add(dCdP[5][3].multiply(paDot)).
1047 add(dCdP[5][4].multiply(raanDot)).
1048 add(dCdP[5][5].multiply(nonKeplerianMeanMotion));
1049
1050 return new FieldVector3D<>(nonKeplerianAx, nonKeplerianAy, nonKeplerianAz);
1051
1052 }
1053
1054
1055 @Override
1056 protected FieldVector3D<T> initPosition() {
1057 final FieldVector3D<T>[] axes = referenceAxes();
1058
1059 if (isElliptical()) {
1060
1061
1062
1063
1064 final T uME2 = e.negate().add(1).multiply(e.add(1));
1065 final T s1Me2 = uME2.sqrt();
1066 final FieldSinCos<T> scE = FastMath.sinCos(getEccentricAnomaly());
1067 final T cosE = scE.cos();
1068 final T sinE = scE.sin();
1069
1070 return new FieldVector3D<>(a.multiply(cosE.subtract(e)), axes[0], a.multiply(sinE).multiply(s1Me2), axes[1]);
1071
1072 } else {
1073
1074
1075
1076
1077 final FieldSinCos<T> scV = FastMath.sinCos(getTrueAnomaly());
1078 final T sinV = scV.sin();
1079 final T cosV = scV.cos();
1080 final T f = a.multiply(e.square().negate().add(1));
1081 final T posFactor = f.divide(e.multiply(cosV).add(1));
1082
1083 return new FieldVector3D<>(posFactor.multiply(cosV), axes[0], posFactor.multiply(sinV), axes[1]);
1084
1085 }
1086
1087 }
1088
1089
1090 @Override
1091 protected TimeStampedFieldPVCoordinates<T> initPVCoordinates() {
1092
1093
1094 computePVWithoutA();
1095
1096
1097 final T r2 = partialPV.getPosition().getNormSq();
1098 final FieldVector3D<T> keplerianAcceleration = new FieldVector3D<>(r2.multiply(FastMath.sqrt(r2)).reciprocal().multiply(getMu().negate()),
1099 partialPV.getPosition());
1100 final FieldVector3D<T> acceleration = hasNonKeplerianRates() ?
1101 keplerianAcceleration.add(nonKeplerianAcceleration()) :
1102 keplerianAcceleration;
1103
1104 return new TimeStampedFieldPVCoordinates<>(getDate(), partialPV.getPosition(), partialPV.getVelocity(), acceleration);
1105
1106 }
1107
1108
1109 @Override
1110 public FieldKeplerianOrbit<T> inFrame(final Frame inertialFrame) {
1111 final FieldPVCoordinates<T> fieldPVCoordinates;
1112 if (hasNonKeplerianAcceleration()) {
1113 fieldPVCoordinates = getPVCoordinates(inertialFrame);
1114 } else {
1115 final FieldKinematicTransform<T> transform = getFrame().getKinematicTransformTo(inertialFrame, getDate());
1116 fieldPVCoordinates = transform.transformOnlyPV(getPVCoordinates());
1117 }
1118 final FieldKeplerianOrbit<T> fieldOrbit = new FieldKeplerianOrbit<>(fieldPVCoordinates, inertialFrame, getDate(), getMu());
1119 if (fieldOrbit.getCachedPositionAngleType() == getCachedPositionAngleType()) {
1120 return fieldOrbit;
1121 } else {
1122 return fieldOrbit.withCachedPositionAngleType(getCachedPositionAngleType());
1123 }
1124 }
1125
1126
1127 @Override
1128 public FieldKeplerianOrbit<T> withCachedPositionAngleType(final PositionAngleType positionAngleType) {
1129 return new FieldKeplerianOrbit<>(a, e, i, pa, raan, getAnomaly(positionAngleType), aDot, eDot, iDot, paDot, raanDot,
1130 getAnomalyDot(positionAngleType), positionAngleType, getFrame(), getDate(), getMu());
1131 }
1132
1133
1134 @Override
1135 public FieldKeplerianOrbit<T> shiftedBy(final double dt) {
1136 return shiftedBy(getZero().newInstance(dt));
1137 }
1138
1139
1140 @Override
1141 public FieldKeplerianOrbit<T> shiftedBy(final T dt) {
1142
1143
1144 final FieldKeplerianOrbit<T> keplerianShifted = new FieldKeplerianOrbit<>(a, e, i, pa, raan,
1145 getKeplerianMeanMotion().multiply(dt).add(getMeanAnomaly()),
1146 PositionAngleType.MEAN, cachedPositionAngleType, getFrame(), getDate().shiftedBy(dt), getMu());
1147
1148 if (hasNonKeplerianRates()) {
1149
1150
1151 final FieldVector3D<T> nonKeplerianAcceleration = nonKeplerianAcceleration();
1152
1153
1154 keplerianShifted.computePVWithoutA();
1155 final FieldVector3D<T> fixedP = new FieldVector3D<>(getOne(), keplerianShifted.partialPV.getPosition(),
1156 dt.square().multiply(0.5), nonKeplerianAcceleration);
1157 final T fixedR2 = fixedP.getNormSq();
1158 final T fixedR = fixedR2.sqrt();
1159 final FieldVector3D<T> fixedV = new FieldVector3D<>(getOne(), keplerianShifted.partialPV.getVelocity(),
1160 dt, nonKeplerianAcceleration);
1161 final FieldVector3D<T> fixedA = new FieldVector3D<>(fixedR2.multiply(fixedR).reciprocal().multiply(getMu().negate()),
1162 keplerianShifted.partialPV.getPosition(),
1163 getOne(), nonKeplerianAcceleration);
1164
1165
1166 return new FieldKeplerianOrbit<>(new TimeStampedFieldPVCoordinates<>(keplerianShifted.getDate(),
1167 fixedP, fixedV, fixedA),
1168 keplerianShifted.getFrame(), keplerianShifted.getMu());
1169
1170 } else {
1171
1172 return keplerianShifted;
1173 }
1174
1175 }
1176
1177
1178 @Override
1179 protected T[][] computeJacobianMeanWrtCartesian() {
1180 if (isElliptical()) {
1181 return computeJacobianMeanWrtCartesianElliptical();
1182 } else {
1183 return computeJacobianMeanWrtCartesianHyperbolic();
1184 }
1185 }
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195 private T[][] computeJacobianMeanWrtCartesianElliptical() {
1196
1197 final T[][] jacobian = MathArrays.buildArray(getA().getField(), 6, 6);
1198
1199
1200 computePVWithoutA();
1201 final FieldVector3D<T> position = partialPV.getPosition();
1202 final FieldVector3D<T> velocity = partialPV.getVelocity();
1203 final FieldVector3D<T> momentum = partialPV.getMomentum();
1204 final T v2 = velocity.getNormSq();
1205 final T r2 = position.getNormSq();
1206 final T r = r2.sqrt();
1207 final T r3 = r.multiply(r2);
1208
1209 final T px = position.getX();
1210 final T py = position.getY();
1211 final T pz = position.getZ();
1212 final T vx = velocity.getX();
1213 final T vy = velocity.getY();
1214 final T vz = velocity.getZ();
1215 final T mx = momentum.getX();
1216 final T my = momentum.getY();
1217 final T mz = momentum.getZ();
1218
1219 final T mu = getMu();
1220 final T sqrtMuA = FastMath.sqrt(a.multiply(mu));
1221 final T sqrtAoMu = FastMath.sqrt(a.divide(mu));
1222 final T a2 = a.square();
1223 final T twoA = a.multiply(2);
1224 final T rOnA = r.divide(a);
1225
1226 final T oMe2 = e.square().negate().add(1);
1227 final T epsilon = oMe2.sqrt();
1228 final T sqrtRec = epsilon.reciprocal();
1229
1230 final FieldSinCos<T> scI = FastMath.sinCos(i);
1231 final FieldSinCos<T> scPA = FastMath.sinCos(pa);
1232 final T cosI = scI.cos();
1233 final T sinI = scI.sin();
1234 final T cosPA = scPA.cos();
1235 final T sinPA = scPA.sin();
1236
1237 final T pv = FieldVector3D.dotProduct(position, velocity);
1238 final T cosE = a.subtract(r).divide(a.multiply(e));
1239 final T sinE = pv.divide(e.multiply(sqrtMuA));
1240
1241
1242 final FieldVector3D<T> vectorAR = new FieldVector3D<>(a2.multiply(2).divide(r3), position);
1243 final FieldVector3D<T> vectorARDot = velocity.scalarMultiply(a2.multiply(mu.divide(2.).reciprocal()));
1244 fillHalfRow(getOne(), vectorAR, jacobian[0], 0);
1245 fillHalfRow(getOne(), vectorARDot, jacobian[0], 3);
1246
1247
1248 final T factorER3 = pv.divide(twoA);
1249 final FieldVector3D<T> vectorER = new FieldVector3D<>(cosE.multiply(v2).divide(r.multiply(mu)), position,
1250 sinE.divide(sqrtMuA), velocity,
1251 factorER3.negate().multiply(sinE).divide(sqrtMuA), vectorAR);
1252 final FieldVector3D<T> vectorERDot = new FieldVector3D<>(sinE.divide(sqrtMuA), position,
1253 cosE.multiply(mu.divide(2.).reciprocal()).multiply(r), velocity,
1254 factorER3.negate().multiply(sinE).divide(sqrtMuA), vectorARDot);
1255 fillHalfRow(getOne(), vectorER, jacobian[1], 0);
1256 fillHalfRow(getOne(), vectorERDot, jacobian[1], 3);
1257
1258
1259 final T coefE = cosE.divide(e.multiply(sqrtMuA));
1260 final FieldVector3D<T> vectorEAnR =
1261 new FieldVector3D<>(sinE.negate().multiply(v2).divide(e.multiply(r).multiply(mu)), position, coefE, velocity,
1262 factorER3.negate().multiply(coefE), vectorAR);
1263
1264
1265 final FieldVector3D<T> vectorEAnRDot =
1266 new FieldVector3D<>(sinE.multiply(-2).multiply(r).divide(e.multiply(mu)), velocity, coefE, position,
1267 factorER3.negate().multiply(coefE), vectorARDot);
1268
1269
1270 final T s1 = sinE.negate().multiply(pz).divide(r).subtract(cosE.multiply(vz).multiply(sqrtAoMu));
1271 final T s2 = cosE.negate().multiply(pz).divide(r3);
1272 final T s3 = sinE.multiply(vz).divide(sqrtMuA.multiply(-2));
1273 final T t1 = sqrtRec.multiply(cosE.multiply(pz).divide(r).subtract(sinE.multiply(vz).multiply(sqrtAoMu)));
1274 final T t2 = sqrtRec.multiply(sinE.negate().multiply(pz).divide(r3));
1275 final T t3 = sqrtRec.multiply(cosE.subtract(e)).multiply(vz).divide(sqrtMuA.multiply(2));
1276 final T t4 = sqrtRec.multiply(e.multiply(sinI).multiply(cosPA).multiply(sqrtRec).subtract(vz.multiply(sqrtAoMu)));
1277 final FieldVector3D<T> s = new FieldVector3D<>(cosE.divide(r), this.PLUS_K,
1278 s1, vectorEAnR,
1279 s2, position,
1280 s3, vectorAR);
1281 final FieldVector3D<T> sDot = new FieldVector3D<>(sinE.negate().multiply(sqrtAoMu), this.PLUS_K,
1282 s1, vectorEAnRDot,
1283 s3, vectorARDot);
1284 final FieldVector3D<T> t =
1285 new FieldVector3D<>(sqrtRec.multiply(sinE).divide(r), this.PLUS_K).add(new FieldVector3D<>(t1, vectorEAnR,
1286 t2, position,
1287 t3, vectorAR,
1288 t4, vectorER));
1289 final FieldVector3D<T> tDot = new FieldVector3D<>(sqrtRec.multiply(cosE.subtract(e)).multiply(sqrtAoMu), this.PLUS_K,
1290 t1, vectorEAnRDot,
1291 t3, vectorARDot,
1292 t4, vectorERDot);
1293
1294
1295 final T factorI1 = sinI.negate().multiply(sqrtRec).divide(sqrtMuA);
1296 final T i1 = factorI1;
1297 final T i2 = factorI1.negate().multiply(mz).divide(twoA);
1298 final T i3 = factorI1.multiply(mz).multiply(e).divide(oMe2);
1299 final T i4 = cosI.multiply(sinPA);
1300 final T i5 = cosI.multiply(cosPA);
1301 fillHalfRow(i1, new FieldVector3D<>(vy, vx.negate(), getZero()), i2, vectorAR, i3, vectorER, i4, s, i5, t,
1302 jacobian[2], 0);
1303 fillHalfRow(i1, new FieldVector3D<>(py.negate(), px, getZero()), i2, vectorARDot, i3, vectorERDot, i4, sDot, i5, tDot,
1304 jacobian[2], 3);
1305
1306
1307 fillHalfRow(cosPA.divide(sinI), s, sinPA.negate().divide(sinI), t, jacobian[3], 0);
1308 fillHalfRow(cosPA.divide(sinI), sDot, sinPA.negate().divide(sinI), tDot, jacobian[3], 3);
1309
1310
1311 final T factorRaanR = (a.multiply(mu).multiply(oMe2).multiply(sinI).multiply(sinI)).reciprocal();
1312 fillHalfRow( factorRaanR.negate().multiply(my), new FieldVector3D<>(getZero(), vz, vy.negate()),
1313 factorRaanR.multiply(mx), new FieldVector3D<>(vz.negate(), getZero(), vx),
1314 jacobian[4], 0);
1315 fillHalfRow(factorRaanR.negate().multiply(my), new FieldVector3D<>(getZero(), pz.negate(), py),
1316 factorRaanR.multiply(mx), new FieldVector3D<>(pz, getZero(), px.negate()),
1317 jacobian[4], 3);
1318
1319
1320 fillHalfRow(rOnA, vectorEAnR, sinE.negate(), vectorER, jacobian[5], 0);
1321 fillHalfRow(rOnA, vectorEAnRDot, sinE.negate(), vectorERDot, jacobian[5], 3);
1322
1323 return jacobian;
1324
1325 }
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335 private T[][] computeJacobianMeanWrtCartesianHyperbolic() {
1336
1337 final T[][] jacobian = MathArrays.buildArray(getA().getField(), 6, 6);
1338
1339
1340 computePVWithoutA();
1341 final FieldVector3D<T> position = partialPV.getPosition();
1342 final FieldVector3D<T> velocity = partialPV.getVelocity();
1343 final FieldVector3D<T> momentum = partialPV.getMomentum();
1344 final T r2 = position.getNormSq();
1345 final T r = r2.sqrt();
1346 final T r3 = r.multiply(r2);
1347
1348 final T x = position.getX();
1349 final T y = position.getY();
1350 final T z = position.getZ();
1351 final T vx = velocity.getX();
1352 final T vy = velocity.getY();
1353 final T vz = velocity.getZ();
1354 final T mx = momentum.getX();
1355 final T my = momentum.getY();
1356 final T mz = momentum.getZ();
1357
1358 final T mu = getMu();
1359 final T absA = a.negate();
1360 final T sqrtMuA = absA.multiply(mu).sqrt();
1361 final T a2 = a.square();
1362 final T rOa = r.divide(absA);
1363
1364 final FieldSinCos<T> scI = FastMath.sinCos(i);
1365 final T cosI = scI.cos();
1366 final T sinI = scI.sin();
1367
1368 final T pv = FieldVector3D.dotProduct(position, velocity);
1369
1370
1371 final FieldVector3D<T> vectorAR = new FieldVector3D<>(a2.multiply(-2).divide(r3), position);
1372 final FieldVector3D<T> vectorARDot = velocity.scalarMultiply(a2.multiply(-2).divide(mu));
1373 fillHalfRow(getOne().negate(), vectorAR, jacobian[0], 0);
1374 fillHalfRow(getOne().negate(), vectorARDot, jacobian[0], 3);
1375
1376
1377 final T m = momentum.getNorm();
1378 final T oOm = m.reciprocal();
1379 final FieldVector3D<T> dcXP = new FieldVector3D<>(getZero(), vz, vy.negate());
1380 final FieldVector3D<T> dcYP = new FieldVector3D<>(vz.negate(), getZero(), vx);
1381 final FieldVector3D<T> dcZP = new FieldVector3D<>( vy, vx.negate(), getZero());
1382 final FieldVector3D<T> dcXV = new FieldVector3D<>( getZero(), z.negate(), y);
1383 final FieldVector3D<T> dcYV = new FieldVector3D<>( z, getZero(), x.negate());
1384 final FieldVector3D<T> dcZV = new FieldVector3D<>( y.negate(), x, getZero());
1385 final FieldVector3D<T> dCP = new FieldVector3D<>(mx.multiply(oOm), dcXP, my.multiply(oOm), dcYP, mz.multiply(oOm), dcZP);
1386 final FieldVector3D<T> dCV = new FieldVector3D<>(mx.multiply(oOm), dcXV, my.multiply(oOm), dcYV, mz.multiply(oOm), dcZV);
1387
1388
1389 final T mOMu = m.divide(mu);
1390 final FieldVector3D<T> dpP = new FieldVector3D<>(mOMu.multiply(2), dCP);
1391 final FieldVector3D<T> dpV = new FieldVector3D<>(mOMu.multiply(2), dCV);
1392
1393
1394 final T p = m.multiply(mOMu);
1395 final T moO2ae = absA.multiply(2).multiply(e).reciprocal();
1396 final T m2OaMu = p.negate().divide(absA);
1397 fillHalfRow(moO2ae, dpP, m2OaMu.multiply(moO2ae), vectorAR, jacobian[1], 0);
1398 fillHalfRow(moO2ae, dpV, m2OaMu.multiply(moO2ae), vectorARDot, jacobian[1], 3);
1399
1400
1401 final T cI1 = m.multiply(sinI).reciprocal();
1402 final T cI2 = cosI.multiply(cI1);
1403 fillHalfRow(cI2, dCP, cI1.negate(), dcZP, jacobian[2], 0);
1404 fillHalfRow(cI2, dCV, cI1.negate(), dcZV, jacobian[2], 3);
1405
1406
1407
1408 final T cP1 = y.multiply(oOm);
1409 final T cP2 = x.negate().multiply(oOm);
1410 final T cP3 = mx.multiply(cP1).add(my.multiply(cP2)).negate();
1411 final T cP4 = cP3.multiply(oOm);
1412 final T cP5 = r2.multiply(sinI).multiply(sinI).negate().reciprocal();
1413 final T cP6 = z.multiply(cP5);
1414 final T cP7 = cP3.multiply(cP5);
1415 final FieldVector3D<T> dacP = new FieldVector3D<>(cP1, dcXP, cP2, dcYP, cP4, dCP, oOm, new FieldVector3D<>(my.negate(), mx, getZero()));
1416 final FieldVector3D<T> dacV = new FieldVector3D<>(cP1, dcXV, cP2, dcYV, cP4, dCV);
1417 final FieldVector3D<T> dpoP = new FieldVector3D<>(cP6, dacP, cP7, this.PLUS_K);
1418 final FieldVector3D<T> dpoV = new FieldVector3D<>(cP6, dacV);
1419
1420 final T re2 = r2.multiply(e.square());
1421 final T recOre2 = p.subtract(r).divide(re2);
1422 final T resOre2 = pv.multiply(mOMu).divide(re2);
1423 final FieldVector3D<T> dreP = new FieldVector3D<>(mOMu, velocity, pv.divide(mu), dCP);
1424 final FieldVector3D<T> dreV = new FieldVector3D<>(mOMu, position, pv.divide(mu), dCV);
1425 final FieldVector3D<T> davP = new FieldVector3D<>(resOre2.negate(), dpP, recOre2, dreP, resOre2.divide(r), position);
1426 final FieldVector3D<T> davV = new FieldVector3D<>(resOre2.negate(), dpV, recOre2, dreV);
1427 fillHalfRow(getOne(), dpoP, getOne().negate(), davP, jacobian[3], 0);
1428 fillHalfRow(getOne(), dpoV, getOne().negate(), davV, jacobian[3], 3);
1429
1430
1431 final T cO0 = cI1.square();
1432 final T cO1 = mx.multiply(cO0);
1433 final T cO2 = my.negate().multiply(cO0);
1434 fillHalfRow(cO1, dcYP, cO2, dcXP, jacobian[4], 0);
1435 fillHalfRow(cO1, dcYV, cO2, dcXV, jacobian[4], 3);
1436
1437
1438 final T s2a = pv.divide(absA.multiply(2));
1439 final T oObux = m.square().add(absA.multiply(mu)).sqrt().reciprocal();
1440 final T scasbu = pv.multiply(oObux);
1441 final FieldVector3D<T> dauP = new FieldVector3D<>(sqrtMuA.reciprocal(), velocity, s2a.negate().divide(sqrtMuA), vectorAR);
1442 final FieldVector3D<T> dauV = new FieldVector3D<>(sqrtMuA.reciprocal(), position, s2a.negate().divide(sqrtMuA), vectorARDot);
1443 final FieldVector3D<T> dbuP = new FieldVector3D<>(oObux.multiply(mu.divide(2.)), vectorAR, m.multiply(oObux), dCP);
1444 final FieldVector3D<T> dbuV = new FieldVector3D<>(oObux.multiply(mu.divide(2.)), vectorARDot, m.multiply(oObux), dCV);
1445 final FieldVector3D<T> dcuP = new FieldVector3D<>(oObux, velocity, scasbu.negate().multiply(oObux), dbuP);
1446 final FieldVector3D<T> dcuV = new FieldVector3D<>(oObux, position, scasbu.negate().multiply(oObux), dbuV);
1447 fillHalfRow(getOne(), dauP, e.negate().divide(rOa.add(1)), dcuP, jacobian[5], 0);
1448 fillHalfRow(getOne(), dauV, e.negate().divide(rOa.add(1)), dcuV, jacobian[5], 3);
1449
1450 return jacobian;
1451
1452 }
1453
1454
1455 @Override
1456 protected T[][] computeJacobianEccentricWrtCartesian() {
1457 if (isElliptical()) {
1458 return computeJacobianEccentricWrtCartesianElliptical();
1459 } else {
1460 return computeJacobianEccentricWrtCartesianHyperbolic();
1461 }
1462 }
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472 private T[][] computeJacobianEccentricWrtCartesianElliptical() {
1473
1474
1475 final T[][] jacobian = computeJacobianMeanWrtCartesianElliptical();
1476
1477
1478
1479
1480
1481 final FieldSinCos<T> scE = FastMath.sinCos(getEccentricAnomaly());
1482 final T aOr = e.negate().multiply(scE.cos()).add(1).reciprocal();
1483
1484
1485 final T[] eRow = jacobian[1];
1486 final T[] anomalyRow = jacobian[5];
1487 for (int j = 0; j < anomalyRow.length; ++j) {
1488 anomalyRow[j] = aOr.multiply(anomalyRow[j].add(scE.sin().multiply(eRow[j])));
1489 }
1490
1491 return jacobian;
1492
1493 }
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503 private T[][] computeJacobianEccentricWrtCartesianHyperbolic() {
1504
1505
1506 final T[][] jacobian = computeJacobianMeanWrtCartesianHyperbolic();
1507
1508
1509
1510
1511
1512 final T H = getEccentricAnomaly();
1513 final T coshH = H.cosh();
1514 final T sinhH = H.sinh();
1515 final T absaOr = e.multiply(coshH).subtract(1).reciprocal();
1516
1517 final T[] eRow = jacobian[1];
1518 final T[] anomalyRow = jacobian[5];
1519
1520 for (int j = 0; j < anomalyRow.length; ++j) {
1521 anomalyRow[j] = absaOr.multiply(anomalyRow[j].subtract(sinhH.multiply(eRow[j])));
1522
1523 }
1524
1525 return jacobian;
1526
1527 }
1528
1529
1530 @Override
1531 protected T[][] computeJacobianTrueWrtCartesian() {
1532 if (isElliptical()) {
1533 return computeJacobianTrueWrtCartesianElliptical();
1534 } else {
1535 return computeJacobianTrueWrtCartesianHyperbolic();
1536 }
1537 }
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547 private T[][] computeJacobianTrueWrtCartesianElliptical() {
1548
1549
1550 final T[][] jacobian = computeJacobianEccentricWrtCartesianElliptical();
1551
1552
1553
1554
1555
1556 final T e2 = e.square();
1557 final T oMe2 = e2.negate().add(1);
1558 final T epsilon = oMe2.sqrt();
1559 final FieldSinCos<T> scE = FastMath.sinCos(getEccentricAnomaly());
1560 final T aOr = e.multiply(scE.cos()).negate().add(1).reciprocal();
1561 final T aFactor = epsilon.multiply(aOr);
1562 final T eFactor = scE.sin().multiply(aOr).divide(epsilon);
1563
1564
1565 final T[] eRow = jacobian[1];
1566 final T[] anomalyRow = jacobian[5];
1567 for (int j = 0; j < anomalyRow.length; ++j) {
1568 anomalyRow[j] = aFactor.multiply(anomalyRow[j]).add(eFactor.multiply(eRow[j]));
1569 }
1570 return jacobian;
1571
1572 }
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582 private T[][] computeJacobianTrueWrtCartesianHyperbolic() {
1583
1584
1585 final T[][] jacobian = computeJacobianEccentricWrtCartesianHyperbolic();
1586
1587
1588
1589
1590
1591
1592 final T e2 = e.square();
1593 final T e2Mo = e2.subtract(1);
1594 final T epsilon = e2Mo.sqrt();
1595 final T H = getEccentricAnomaly();
1596 final T coshH = H.cosh();
1597 final T sinhH = H.sinh();
1598 final T aOr = e.multiply(coshH).subtract(1).reciprocal();
1599 final T aFactor = epsilon.multiply(aOr);
1600 final T eFactor = sinhH.multiply(aOr).divide(epsilon);
1601
1602
1603 final T[] eRow = jacobian[1];
1604 final T[] anomalyRow = jacobian[5];
1605 for (int j = 0; j < anomalyRow.length; ++j) {
1606 anomalyRow[j] = aFactor.multiply(anomalyRow[j]).subtract(eFactor.multiply(eRow[j]));
1607 }
1608
1609 return jacobian;
1610
1611 }
1612
1613
1614 @Override
1615 public void addKeplerContribution(final PositionAngleType type, final T gm,
1616 final T[] pDot) {
1617 pDot[5] = pDot[5].add(computeKeplerianAnomalyDot(type, a, e, gm, cachedAnomaly, cachedPositionAngleType));
1618 }
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632 private static <T extends CalculusFieldElement<T>> T computeKeplerianAnomalyDot(final PositionAngleType type, final T a, final T e,
1633 final T mu, final T anomaly, final PositionAngleType cachedType) {
1634 final T absA = a.abs();
1635 final T n = absA.reciprocal().multiply(mu).sqrt().divide(absA);
1636 if (type == PositionAngleType.MEAN) {
1637 return n;
1638 }
1639 final T ksi;
1640 final T oMe2;
1641 final T trueAnomaly = FieldKeplerianAnomalyUtility.convertAnomaly(cachedType, anomaly, e, PositionAngleType.TRUE);
1642 if (type == PositionAngleType.ECCENTRIC) {
1643 oMe2 = e.square().negate().add(1).abs();
1644 ksi = e.multiply(trueAnomaly.cos()).add(1);
1645 return n.multiply(ksi).divide(oMe2);
1646 } else {
1647 oMe2 = e.square().negate().add(1).abs();
1648 ksi = e.multiply(trueAnomaly.cos()).add(1);
1649 return n.multiply(ksi).multiply(ksi).divide(oMe2.multiply(oMe2.sqrt()));
1650 }
1651 }
1652
1653
1654
1655
1656 public String toString() {
1657 return new StringBuilder().append("Keplerian parameters: ").append('{').
1658 append("a: ").append(a.getReal()).
1659 append("; e: ").append(e.getReal()).
1660 append("; i: ").append(FastMath.toDegrees(i.getReal())).
1661 append("; pa: ").append(FastMath.toDegrees(pa.getReal())).
1662 append("; raan: ").append(FastMath.toDegrees(raan.getReal())).
1663 append("; v: ").append(FastMath.toDegrees(getTrueAnomaly().getReal())).
1664 append(";}").toString();
1665 }
1666
1667
1668 @Override
1669 public PositionAngleType getCachedPositionAngleType() {
1670 return cachedPositionAngleType;
1671 }
1672
1673
1674 @Override
1675 public boolean hasNonKeplerianRates() {
1676 return hasNonKeplerianAcceleration();
1677 }
1678
1679
1680 @Override
1681 public FieldKeplerianOrbit<T> withKeplerianRates() {
1682 return new FieldKeplerianOrbit<>(getA(), getE(), getI(), getPerigeeArgument(), getRightAscensionOfAscendingNode(),
1683 cachedAnomaly, cachedPositionAngleType, getFrame(), getDate(), getMu());
1684 }
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700 private void checkParameterRangeInclusive(final String parameterName, final double parameter,
1701 final double lowerBound, final double upperBound) {
1702 if (parameter < lowerBound || parameter > upperBound) {
1703 throw new OrekitException(OrekitMessages.INVALID_PARAMETER_RANGE, parameterName,
1704 parameter, lowerBound, upperBound);
1705 }
1706 }
1707
1708
1709 @Override
1710 public KeplerianOrbit toOrbit() {
1711 final double cachedPositionAngle = cachedAnomaly.getReal();
1712 return new KeplerianOrbit(a.getReal(), e.getReal(), i.getReal(),
1713 pa.getReal(), raan.getReal(), cachedPositionAngle,
1714 aDot.getReal(), eDot.getReal(), iDot.getReal(),
1715 paDot.getReal(), raanDot.getReal(),
1716 cachedAnomalyDot.getReal(),
1717 cachedPositionAngleType, cachedPositionAngleType,
1718 getFrame(), getDate().toAbsoluteDate(), getMu().getReal());
1719 }
1720
1721
1722 }