TimeStampedFieldAngularCoordinates.java

  1. /* Copyright 2002-2019 CS Systèmes d'Information
  2.  * Licensed to CS Systèmes d'Information (CS) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * CS licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *   http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.orekit.utils;

  19. import java.util.Collection;

  21. import org.hipparchus.Field;
  22. import org.hipparchus.RealFieldElement;
  23. import org.hipparchus.analysis.differentiation.FieldDerivativeStructure;
  24. import org.hipparchus.analysis.interpolation.FieldHermiteInterpolator;
  25. import org.hipparchus.geometry.euclidean.threed.FieldRotation;
  26. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  27. import org.hipparchus.geometry.euclidean.threed.RotationConvention;
  28. import org.hipparchus.util.FastMath;
  29. import org.orekit.errors.OrekitException;
  30. import org.orekit.errors.OrekitInternalError;
  31. import org.orekit.errors.OrekitMessages;
  32. import org.orekit.time.AbsoluteDate;
  33. import org.orekit.time.FieldAbsoluteDate;
  34. import org.orekit.time.TimeStamped;

  36. /** {@link TimeStamped time-stamped} version of {@link FieldAngularCoordinates}.
  37.  * <p>Instances of this class are guaranteed to be immutable.</p>
  38.  * @param <T> the type of the field elements
  39.  * @author Luc Maisonobe
  40.  * @since 7.0
  41.  */
  42. public class TimeStampedFieldAngularCoordinates<T extends RealFieldElement<T>>
  43.     extends FieldAngularCoordinates<T> {

  45.     /** The date. */
  46.     private final FieldAbsoluteDate<T> date;

  48.     /** Build the rotation that transforms a pair of pv coordinates into another pair.

  50.      * <p><em>WARNING</em>! This method requires much more stringent assumptions on
  51.      * its parameters than the similar {@link org.hipparchus.geometry.euclidean.threed.Rotation#Rotation(
  52.      * org.hipparchus.geometry.euclidean.threed.Vector3D, org.hipparchus.geometry.euclidean.threed.Vector3D,
  53.      * org.hipparchus.geometry.euclidean.threed.Vector3D, org.hipparchus.geometry.euclidean.threed.Vector3D)
  54.      * constructor} from the {@link org.hipparchus.geometry.euclidean.threed.Rotation Rotation} class.
  55.      * As far as the Rotation constructor is concerned, the {@code v₂} vector from
  56.      * the second pair can be slightly misaligned. The Rotation constructor will
  57.      * compensate for this misalignment and create a rotation that ensure {@code
  58.      * v₁ = r(u₁)} and {@code v₂ ∈ plane (r(u₁), r(u₂))}. <em>THIS IS NOT
  59.      * TRUE ANYMORE IN THIS CLASS</em>! As derivatives are involved and must be
  60.      * preserved, this constructor works <em>only</em> if the two pairs are fully
  61.      * consistent, i.e. if a rotation exists that fulfill all the requirements: {@code
  62.      * v₁ = r(u₁)}, {@code v₂ = r(u₂)}, {@code dv₁/dt = dr(u₁)/dt}, {@code dv₂/dt
  63.      * = dr(u₂)/dt}, {@code d²v₁/dt² = d²r(u₁)/dt²}, {@code d²v₂/dt² = d²r(u₂)/dt²}.</p>

  65.      * @param date coordinates date
  66.      * @param u1 first vector of the origin pair
  67.      * @param u2 second vector of the origin pair
  68.      * @param v1 desired image of u1 by the rotation
  69.      * @param v2 desired image of u2 by the rotation
  70.      * @param tolerance relative tolerance factor used to check singularities
  71.      */
  72.     public TimeStampedFieldAngularCoordinates (final AbsoluteDate date,
  73.                                                final FieldPVCoordinates<T> u1, final FieldPVCoordinates<T> u2,
  74.                                                final FieldPVCoordinates<T> v1, final FieldPVCoordinates<T> v2,
  75.                                                final double tolerance) {
  76.         this(new FieldAbsoluteDate<>(u1.getPosition().getX().getField(), date),
  77.              u1, u2, v1, v2, tolerance);
  78.     }

  80.     /** Build the rotation that transforms a pair of pv coordinates into another pair.

  82.      * <p><em>WARNING</em>! This method requires much more stringent assumptions on
  83.      * its parameters than the similar {@link org.hipparchus.geometry.euclidean.threed.Rotation#Rotation(
  84.      * org.hipparchus.geometry.euclidean.threed.Vector3D, org.hipparchus.geometry.euclidean.threed.Vector3D,
  85.      * org.hipparchus.geometry.euclidean.threed.Vector3D, org.hipparchus.geometry.euclidean.threed.Vector3D)
  86.      * constructor} from the {@link org.hipparchus.geometry.euclidean.threed.Rotation Rotation} class.
  87.      * As far as the Rotation constructor is concerned, the {@code v₂} vector from
  88.      * the second pair can be slightly misaligned. The Rotation constructor will
  89.      * compensate for this misalignment and create a rotation that ensure {@code
  90.      * v₁ = r(u₁)} and {@code v₂ ∈ plane (r(u₁), r(u₂))}. <em>THIS IS NOT
  91.      * TRUE ANYMORE IN THIS CLASS</em>! As derivatives are involved and must be
  92.      * preserved, this constructor works <em>only</em> if the two pairs are fully
  93.      * consistent, i.e. if a rotation exists that fulfill all the requirements: {@code
  94.      * v₁ = r(u₁)}, {@code v₂ = r(u₂)}, {@code dv₁/dt = dr(u₁)/dt}, {@code dv₂/dt
  95.      * = dr(u₂)/dt}, {@code d²v₁/dt² = d²r(u₁)/dt²}, {@code d²v₂/dt² = d²r(u₂)/dt²}.</p>

  97.      * @param date coordinates date
  98.      * @param u1 first vector of the origin pair
  99.      * @param u2 second vector of the origin pair
  100.      * @param v1 desired image of u1 by the rotation
  101.      * @param v2 desired image of u2 by the rotation
  102.      * @param tolerance relative tolerance factor used to check singularities
  103.      */
  104.     public TimeStampedFieldAngularCoordinates (final FieldAbsoluteDate<T> date,
  105.                                                final FieldPVCoordinates<T> u1, final FieldPVCoordinates<T> u2,
  106.                                                final FieldPVCoordinates<T> v1, final FieldPVCoordinates<T> v2,
  107.                                                final double tolerance) {
  108.         super(u1, u2, v1, v2, tolerance);
  109.         this.date = date;
  110.     }

  112.     /** Builds a rotation/rotation rate pair.
  113.      * @param date coordinates date
  114.      * @param rotation rotation
  115.      * @param rotationRate rotation rate Ω (rad/s)
  116.      * @param rotationAcceleration rotation acceleration dΩ/dt (rad²/s²)
  117.      */
  118.     public TimeStampedFieldAngularCoordinates(final AbsoluteDate date,
  119.                                               final FieldRotation<T> rotation,
  120.                                               final FieldVector3D<T> rotationRate,
  121.                                               final FieldVector3D<T> rotationAcceleration) {
  122.         this(new FieldAbsoluteDate<>(rotation.getQ0().getField(), date),
  123.              rotation, rotationRate, rotationAcceleration);
  124.     }

  126.     /** Builds a rotation/rotation rate pair.
  127.      * @param date coordinates date
  128.      * @param rotation rotation
  129.      * @param rotationRate rotation rate Ω (rad/s)
  130.      * @param rotationAcceleration rotation acceleration dΩ/dt (rad²/s²)
  131.      */
  132.     public TimeStampedFieldAngularCoordinates(final FieldAbsoluteDate<T> date,
  133.                                               final FieldRotation<T> rotation,
  134.                                               final FieldVector3D<T> rotationRate,
  135.                                               final FieldVector3D<T> rotationAcceleration) {
  136.         super(rotation, rotationRate, rotationAcceleration);
  137.         this.date = date;
  138.     }

  140.     /** Builds an instance for a regular {@link TimeStampedAngularCoordinates}.
  141.      * @param field fields to which the elements belong
  142.      * @param ac coordinates to convert
  143.      * @since 9.0
  144.      */
  145.     public TimeStampedFieldAngularCoordinates(final Field<T> field,
  146.                                               final TimeStampedAngularCoordinates ac) {
  147.         this(new FieldAbsoluteDate<>(field, ac.getDate()),
  148.              new FieldRotation<>(field, ac.getRotation()),
  149.              new FieldVector3D<>(field, ac.getRotationRate()),
  150.              new FieldVector3D<>(field, ac.getRotationAcceleration()));
  151.     }

  153.     /** Builds a TimeStampedFieldAngularCoordinates from  a {@link FieldRotation}&lt;{@link FieldDerivativeStructure}&gt;.
  154.      * <p>
  155.      * The rotation components must have time as their only derivation parameter and
  156.      * have consistent derivation orders.
  157.      * </p>
  158.      * @param date coordinates date
  159.      * @param r rotation with time-derivatives embedded within the coordinates
  160.      * @since 9.2
  161.      */
  162.     public TimeStampedFieldAngularCoordinates(final FieldAbsoluteDate<T> date,
  163.                                               final FieldRotation<FieldDerivativeStructure<T>> r) {
  164.         super(r);
  165.         this.date = date;
  166.     }

  168.     /** Revert a rotation/rotation rate pair.
  169.      * Build a pair which reverse the effect of another pair.
  170.      * @return a new pair whose effect is the reverse of the effect
  171.      * of the instance
  172.      */
  173.     public TimeStampedFieldAngularCoordinates<T> revert() {
  174.         return new TimeStampedFieldAngularCoordinates<>(date,
  175.                                                         getRotation().revert(),
  176.                                                         getRotation().applyInverseTo(getRotationRate().negate()),
  177.                                                         getRotation().applyInverseTo(getRotationAcceleration().negate()));
  178.     }

  180.     /** Get the date.
  181.      * @return date
  182.      */
  183.     public FieldAbsoluteDate<T> getDate() {
  184.         return date;
  185.     }

  187.     /** Get a time-shifted state.
  188.      * <p>
  189.      * The state can be slightly shifted to close dates. This shift is based on
  190.      * a simple linear model. It is <em>not</em> intended as a replacement for
  191.      * proper attitude propagation but should be sufficient for either small
  192.      * time shifts or coarse accuracy.
  193.      * </p>
  194.      * @param dt time shift in seconds
  195.      * @return a new state, shifted with respect to the instance (which is immutable)
  196.      */
  197.     public TimeStampedFieldAngularCoordinates<T> shiftedBy(final double dt) {
  198.         return shiftedBy(getDate().getField().getZero().add(dt));
  199.     }

  201.     /** Get a time-shifted state.
  202.      * <p>
  203.      * The state can be slightly shifted to close dates. This shift is based on
  204.      * a simple linear model. It is <em>not</em> intended as a replacement for
  205.      * proper attitude propagation but should be sufficient for either small
  206.      * time shifts or coarse accuracy.
  207.      * </p>
  208.      * @param dt time shift in seconds
  209.      * @return a new state, shifted with respect to the instance (which is immutable)
  210.      */
  211.     public TimeStampedFieldAngularCoordinates<T> shiftedBy(final T dt) {
  212.         final FieldAngularCoordinates<T> sac = super.shiftedBy(dt);
  213.         return new TimeStampedFieldAngularCoordinates<>(date.shiftedBy(dt),
  214.                                                         sac.getRotation(), sac.getRotationRate(), sac.getRotationAcceleration());

  216.     }

  218.     /** Add an offset from the instance.
  219.      * <p>
  220.      * We consider here that the offset rotation is applied first and the
  221.      * instance is applied afterward. Note that angular coordinates do <em>not</em>
  222.      * commute under this operation, i.e. {@code a.addOffset(b)} and {@code
  223.      * b.addOffset(a)} lead to <em>different</em> results in most cases.
  224.      * </p>
  225.      * <p>
  226.      * The two methods {@link #addOffset(FieldAngularCoordinates) addOffset} and
  227.      * {@link #subtractOffset(FieldAngularCoordinates) subtractOffset} are designed
  228.      * so that round trip applications are possible. This means that both {@code
  229.      * ac1.subtractOffset(ac2).addOffset(ac2)} and {@code
  230.      * ac1.addOffset(ac2).subtractOffset(ac2)} return angular coordinates equal to ac1.
  231.      * </p>
  232.      * @param offset offset to subtract
  233.      * @return new instance, with offset subtracted
  234.      * @see #subtractOffset(FieldAngularCoordinates)
  235.      */
  236.     public TimeStampedFieldAngularCoordinates<T> addOffset(final FieldAngularCoordinates<T> offset) {
  237.         final FieldVector3D<T> rOmega    = getRotation().applyTo(offset.getRotationRate());
  238.         final FieldVector3D<T> rOmegaDot = getRotation().applyTo(offset.getRotationAcceleration());
  239.         return new TimeStampedFieldAngularCoordinates<>(date,
  240.                                                         getRotation().compose(offset.getRotation(), RotationConvention.VECTOR_OPERATOR),
  241.                                                         getRotationRate().add(rOmega),
  242.                                                         new FieldVector3D<>( 1.0, getRotationAcceleration(),
  243.                                                                               1.0, rOmegaDot,
  244.                                                                              -1.0, FieldVector3D.crossProduct(getRotationRate(), rOmega)));
  245.     }

  247.     /** Subtract an offset from the instance.
  248.      * <p>
  249.      * We consider here that the offset Rotation is applied first and the
  250.      * instance is applied afterward. Note that angular coordinates do <em>not</em>
  251.      * commute under this operation, i.e. {@code a.subtractOffset(b)} and {@code
  252.      * b.subtractOffset(a)} lead to <em>different</em> results in most cases.
  253.      * </p>
  254.      * <p>
  255.      * The two methods {@link #addOffset(FieldAngularCoordinates) addOffset} and
  256.      * {@link #subtractOffset(FieldAngularCoordinates) subtractOffset} are designed
  257.      * so that round trip applications are possible. This means that both {@code
  258.      * ac1.subtractOffset(ac2).addOffset(ac2)} and {@code
  259.      * ac1.addOffset(ac2).subtractOffset(ac2)} return angular coordinates equal to ac1.
  260.      * </p>
  261.      * @param offset offset to subtract
  262.      * @return new instance, with offset subtracted
  263.      * @see #addOffset(FieldAngularCoordinates)
  264.      */
  265.     public TimeStampedFieldAngularCoordinates<T> subtractOffset(final FieldAngularCoordinates<T> offset) {
  266.         return addOffset(offset.revert());
  267.     }

  269.     /** Interpolate angular coordinates.
  270.      * <p>
  271.      * The interpolated instance is created by polynomial Hermite interpolation
  272.      * on Rodrigues vector ensuring rotation rate remains the exact derivative of rotation.
  273.      * </p>
  274.      * <p>
  275.      * This method is based on Sergei Tanygin's paper <a
  276.      * href="http://www.agi.com/downloads/resources/white-papers/Attitude-interpolation.pdf">Attitude
  277.      * Interpolation</a>, changing the norm of the vector to match the modified Rodrigues
  278.      * vector as described in Malcolm D. Shuster's paper <a
  279.      * href="http://www.ladispe.polito.it/corsi/Meccatronica/02JHCOR/2011-12/Slides/Shuster_Pub_1993h_J_Repsurv_scan.pdf">A
  280.      * Survey of Attitude Representations</a>. This change avoids the singularity at π.
  281.      * There is still a singularity at 2π, which is handled by slightly offsetting all rotations
  282.      * when this singularity is detected.
  283.      * </p>
  284.      * <p>
  285.      * Note that even if first time derivatives (rotation rates)
  286.      * from sample can be ignored, the interpolated instance always includes
  287.      * interpolated derivatives. This feature can be used explicitly to
  288.      * compute these derivatives when it would be too complex to compute them
  289.      * from an analytical formula: just compute a few sample points from the
  290.      * explicit formula and set the derivatives to zero in these sample points,
  291.      * then use interpolation to add derivatives consistent with the rotations.
  292.      * </p>
  293.      * @param date interpolation date
  294.      * @param filter filter for derivatives from the sample to use in interpolation
  295.      * @param sample sample points on which interpolation should be done
  296.      * @param <T> the type of the field elements
  297.      * @return a new position-velocity, interpolated at specified date
  298.      */
  299.     public static <T extends RealFieldElement<T>>
  300.         TimeStampedFieldAngularCoordinates<T> interpolate(final AbsoluteDate date,
  301.                                                           final AngularDerivativesFilter filter,
  302.                                                           final Collection<TimeStampedFieldAngularCoordinates<T>> sample) {
  303.         return interpolate(new FieldAbsoluteDate<>(sample.iterator().next().getRotation().getQ0().getField(), date),
  304.                            filter, sample);
  305.     }

  307.     /** Interpolate angular coordinates.
  308.      * <p>
  309.      * The interpolated instance is created by polynomial Hermite interpolation
  310.      * on Rodrigues vector ensuring rotation rate remains the exact derivative of rotation.
  311.      * </p>
  312.      * <p>
  313.      * This method is based on Sergei Tanygin's paper <a
  314.      * href="http://www.agi.com/downloads/resources/white-papers/Attitude-interpolation.pdf">Attitude
  315.      * Interpolation</a>, changing the norm of the vector to match the modified Rodrigues
  316.      * vector as described in Malcolm D. Shuster's paper <a
  317.      * href="http://www.ladispe.polito.it/corsi/Meccatronica/02JHCOR/2011-12/Slides/Shuster_Pub_1993h_J_Repsurv_scan.pdf">A
  318.      * Survey of Attitude Representations</a>. This change avoids the singularity at π.
  319.      * There is still a singularity at 2π, which is handled by slightly offsetting all rotations
  320.      * when this singularity is detected.
  321.      * </p>
  322.      * <p>
  323.      * Note that even if first time derivatives (rotation rates)
  324.      * from sample can be ignored, the interpolated instance always includes
  325.      * interpolated derivatives. This feature can be used explicitly to
  326.      * compute these derivatives when it would be too complex to compute them
  327.      * from an analytical formula: just compute a few sample points from the
  328.      * explicit formula and set the derivatives to zero in these sample points,
  329.      * then use interpolation to add derivatives consistent with the rotations.
  330.      * </p>
  331.      * @param date interpolation date
  332.      * @param filter filter for derivatives from the sample to use in interpolation
  333.      * @param sample sample points on which interpolation should be done
  334.      * @param <T> the type of the field elements
  335.      * @return a new position-velocity, interpolated at specified date
  336.      */
  337.     public static <T extends RealFieldElement<T>>
  338.         TimeStampedFieldAngularCoordinates<T> interpolate(final FieldAbsoluteDate<T> date,
  339.                                                           final AngularDerivativesFilter filter,
  340.                                                           final Collection<TimeStampedFieldAngularCoordinates<T>> sample) {

  342.         // get field properties
  343.         final Field<T> field = sample.iterator().next().getRotation().getQ0().getField();

  345.         // set up safety elements for 2π singularity avoidance
  346.         final double epsilon   = 2 * FastMath.PI / sample.size();
  347.         final double threshold = FastMath.min(-(1.0 - 1.0e-4), -FastMath.cos(epsilon / 4));

  349.         // set up a linear model canceling mean rotation rate
  350.         final FieldVector3D<T> meanRate;
  351.         if (filter != AngularDerivativesFilter.USE_R) {
  352.             FieldVector3D<T> sum = FieldVector3D.getZero(field);
  353.             for (final TimeStampedFieldAngularCoordinates<T> datedAC : sample) {
  354.                 sum = sum.add(datedAC.getRotationRate());
  355.             }
  356.             meanRate = new FieldVector3D<>(1.0 / sample.size(), sum);
  357.         } else {
  358.             if (sample.size() < 2) {
  359.                 throw new OrekitException(OrekitMessages.NOT_ENOUGH_DATA_FOR_INTERPOLATION,
  360.                                           sample.size());
  361.             }
  362.             FieldVector3D<T> sum = FieldVector3D.getZero(field);
  363.             TimeStampedFieldAngularCoordinates<T> previous = null;
  364.             for (final TimeStampedFieldAngularCoordinates<T> datedAC : sample) {
  365.                 if (previous != null) {
  366.                     sum = sum.add(estimateRate(previous.getRotation(), datedAC.getRotation(),
  367.                                                datedAC.date.durationFrom(previous.getDate())));
  368.                 }
  369.                 previous = datedAC;
  370.             }
  371.             meanRate = new FieldVector3D<>(1.0 / (sample.size() - 1), sum);
  372.         }
  373.         TimeStampedFieldAngularCoordinates<T> offset =
  374.                 new TimeStampedFieldAngularCoordinates<>(date, FieldRotation.getIdentity(field),
  375.                                                          meanRate, FieldVector3D.getZero(field));

  377.         boolean restart = true;
  378.         for (int i = 0; restart && i < sample.size() + 2; ++i) {

  380.             // offset adaptation parameters
  381.             restart = false;

  383.             // set up an interpolator taking derivatives into account
  384.             final FieldHermiteInterpolator<T> interpolator = new FieldHermiteInterpolator<>();

  386.             // add sample points
  387.             double sign = +1.0;
  388.             FieldRotation<T> previous = FieldRotation.getIdentity(field);

  390.             for (final TimeStampedFieldAngularCoordinates<T> ac : sample) {

  392.                 // remove linear offset from the current coordinates
  393.                 final T dt = ac.date.durationFrom(date);
  394.                 final TimeStampedFieldAngularCoordinates<T> fixed = ac.subtractOffset(offset.shiftedBy(dt));

  396.                 // make sure all interpolated points will be on the same branch
  397.                 final T dot = dt.linearCombination(fixed.getRotation().getQ0(), previous.getQ0(),
  398.                                                    fixed.getRotation().getQ1(), previous.getQ1(),
  399.                                                    fixed.getRotation().getQ2(), previous.getQ2(),
  400.                                                    fixed.getRotation().getQ3(), previous.getQ3());
  401.                 sign = FastMath.copySign(1.0, dot.getReal() * sign);
  402.                 previous = fixed.getRotation();

  404.                 // check modified Rodrigues vector singularity
  405.                 if (fixed.getRotation().getQ0().getReal() * sign < threshold) {
  406.                     // the sample point is close to a modified Rodrigues vector singularity
  407.                     // we need to change the linear offset model to avoid this
  408.                     restart = true;
  409.                     break;
  410.                 }

  412.                 final T[][] rodrigues = fixed.getModifiedRodrigues(sign);
  413.                 switch (filter) {
  414.                     case USE_RRA:
  415.                         // populate sample with rotation, rotation rate and acceleration data
  416.                         interpolator.addSamplePoint(dt, rodrigues[0], rodrigues[1], rodrigues[2]);
  417.                         break;
  418.                     case USE_RR:
  419.                         // populate sample with rotation and rotation rate data
  420.                         interpolator.addSamplePoint(dt, rodrigues[0], rodrigues[1]);
  421.                         break;
  422.                     case USE_R:
  423.                         // populate sample with rotation data only
  424.                         interpolator.addSamplePoint(dt, rodrigues[0]);
  425.                         break;
  426.                     default :
  427.                         // this should never happen
  428.                         throw new OrekitInternalError(null);
  429.                 }
  430.             }

  432.             if (restart) {
  433.                 // interpolation failed, some intermediate rotation was too close to 2π
  434.                 // we need to offset all rotations to avoid the singularity
  435.                 offset = offset.addOffset(new FieldAngularCoordinates<>(new FieldRotation<>(FieldVector3D.getPlusI(field),
  436.                                                                                             field.getZero().add(epsilon),
  437.                                                                                             RotationConvention.VECTOR_OPERATOR),
  438.                                                                         FieldVector3D.getZero(field),
  439.                                                                         FieldVector3D.getZero(field)));
  440.             } else {
  441.                 // interpolation succeeded with the current offset
  442.                 final T[][] p = interpolator.derivatives(field.getZero(), 2);
  443.                 final FieldAngularCoordinates<T> ac = createFromModifiedRodrigues(p);
  444.                 return new TimeStampedFieldAngularCoordinates<>(offset.getDate(),
  445.                                                                 ac.getRotation(),
  446.                                                                 ac.getRotationRate(),
  447.                                                                 ac.getRotationAcceleration()).addOffset(offset);
  448.             }

  450.         }

  452.         // this should never happen
  453.         throw new OrekitInternalError(null);

  455.     }

  457. }
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