Examples with DormandPrince853FieldIntegrator org.hipparchus.ode.nonstiff.DormandPrince853FieldIntegrator used on opensource projects

Example 16 with DormandPrince853FieldIntegrator

use of org.hipparchus.ode.nonstiff.DormandPrince853FieldIntegrator in project Orekit by CS-SI.

the class FieldIntegratedEphemerisTest method createPropagator.

private <T extends RealFieldElement<T>> FieldNumericalPropagator<T> createPropagator(Field<T> field) {
    double[] absTolerance = { 0.0001, 1.0e-11, 1.0e-11, 1.0e-8, 1.0e-8, 1.0e-8, 0.001 };
    double[] relTolerance = { 1.0e-8, 1.0e-8, 1.0e-8, 1.0e-9, 1.0e-9, 1.0e-9, 1.0e-7 };
    OrbitType type = OrbitType.EQUINOCTIAL;
    AdaptiveStepsizeFieldIntegrator<T> integrator = new DormandPrince853FieldIntegrator<>(field, 0.001, 500, absTolerance, relTolerance);
    integrator.setInitialStepSize(field.getZero().add(100));
    FieldNumericalPropagator<T> numericalPropagator = new FieldNumericalPropagator<>(field, integrator);
    numericalPropagator.setOrbitType(type);
    return numericalPropagator;
}

Example 17 with DormandPrince853FieldIntegrator

use of org.hipparchus.ode.nonstiff.DormandPrince853FieldIntegrator in project Orekit by CS-SI.

the class FieldNumericalPropagatorTest method doTestNoExtrapolation.

private <T extends RealFieldElement<T>> void doTestNoExtrapolation(Field<T> field) throws OrekitException {
    T zero = field.getZero();
    // setup
    final FieldAbsoluteDate<T> initDate = FieldAbsoluteDate.getJ2000Epoch(field);
    FieldSpacecraftState<T> initialState;
    FieldNumericalPropagator<T> propagator;
    final FieldVector3D<T> position = new FieldVector3D<>(zero.add(7.0e6), zero.add(1.0e6), zero.add(4.0e6));
    final FieldVector3D<T> velocity = new FieldVector3D<>(zero.add(-500.0), zero.add(8000.0), zero.add(1000.0));
    final FieldOrbit<T> orbit = new FieldEquinoctialOrbit<>(new FieldPVCoordinates<>(position, velocity), FramesFactory.getEME2000(), initDate, mu);
    initialState = new FieldSpacecraftState<>(orbit);
    OrbitType type = OrbitType.EQUINOCTIAL;
    double[][] tolerance = NumericalPropagator.tolerances(0.001, orbit.toOrbit(), type);
    AdaptiveStepsizeFieldIntegrator<T> integrator = new DormandPrince853FieldIntegrator<>(field, 0.001, 200, tolerance[0], tolerance[1]);
    integrator.setInitialStepSize(zero.add(60));
    propagator = new FieldNumericalPropagator<>(field, integrator);
    propagator.setOrbitType(type);
    propagator.setInitialState(initialState);
    // Propagate of the initial at the initial date
    final FieldSpacecraftState<T> finalState = propagator.propagate(initDate);
    // Initial orbit definition
    final FieldVector3D<T> initialPosition = initialState.getPVCoordinates().getPosition();
    final FieldVector3D<T> initialVelocity = initialState.getPVCoordinates().getVelocity();
    // Final orbit definition
    final FieldVector3D<T> finalPosition = finalState.getPVCoordinates().getPosition();
    final FieldVector3D<T> finalVelocity = finalState.getPVCoordinates().getVelocity();
    // Check results
    Assert.assertEquals(initialPosition.getX().getReal(), finalPosition.getX().getReal(), 1.0e-10);
    Assert.assertEquals(initialPosition.getY().getReal(), finalPosition.getY().getReal(), 1.0e-10);
    Assert.assertEquals(initialPosition.getZ().getReal(), finalPosition.getZ().getReal(), 1.0e-10);
    Assert.assertEquals(initialVelocity.getX().getReal(), finalVelocity.getX().getReal(), 1.0e-10);
    Assert.assertEquals(initialVelocity.getY().getReal(), finalVelocity.getY().getReal(), 1.0e-10);
    Assert.assertEquals(initialVelocity.getZ().getReal(), finalVelocity.getZ().getReal(), 1.0e-10);
}

Example 18 with DormandPrince853FieldIntegrator

use of org.hipparchus.ode.nonstiff.DormandPrince853FieldIntegrator in project Orekit by CS-SI.

the class SolarRadiationPressureTest method RealFieldIsotropicTest.

/**
 *Testing if the propagation between the FieldPropagation and the propagation
 * is equivalent.
 * Also testing if propagating X+dX with the propagation is equivalent to
 * propagation X with the FieldPropagation and then applying the taylor
 * expansion of dX to the result.
 */
@Test
public void RealFieldIsotropicTest() throws OrekitException {
    DSFactory factory = new DSFactory(6, 5);
    DerivativeStructure a_0 = factory.variable(0, 7e7);
    DerivativeStructure e_0 = factory.variable(1, 0.4);
    DerivativeStructure i_0 = factory.variable(2, 85 * FastMath.PI / 180);
    DerivativeStructure R_0 = factory.variable(3, 0.7);
    DerivativeStructure O_0 = factory.variable(4, 0.5);
    DerivativeStructure n_0 = factory.variable(5, 0.1);
    Field<DerivativeStructure> field = a_0.getField();
    DerivativeStructure zero = field.getZero();
    FieldAbsoluteDate<DerivativeStructure> J2000 = FieldAbsoluteDate.getJ2000Epoch(field);
    Frame EME = FramesFactory.getEME2000();
    FieldKeplerianOrbit<DerivativeStructure> FKO = new FieldKeplerianOrbit<>(a_0, e_0, i_0, R_0, O_0, n_0, PositionAngle.MEAN, EME, J2000, Constants.EIGEN5C_EARTH_MU);
    FieldSpacecraftState<DerivativeStructure> initialState = new FieldSpacecraftState<>(FKO);
    SpacecraftState iSR = initialState.toSpacecraftState();
    final OrbitType type = OrbitType.KEPLERIAN;
    double[][] tolerance = NumericalPropagator.tolerances(10.0, FKO.toOrbit(), type);
    AdaptiveStepsizeFieldIntegrator<DerivativeStructure> integrator = new DormandPrince853FieldIntegrator<>(field, 0.001, 200, tolerance[0], tolerance[1]);
    integrator.setInitialStepSize(zero.add(60));
    AdaptiveStepsizeIntegrator RIntegrator = new DormandPrince853Integrator(0.001, 200, tolerance[0], tolerance[1]);
    RIntegrator.setInitialStepSize(60);
    FieldNumericalPropagator<DerivativeStructure> FNP = new FieldNumericalPropagator<>(field, integrator);
    FNP.setOrbitType(type);
    FNP.setInitialState(initialState);
    NumericalPropagator NP = new NumericalPropagator(RIntegrator);
    NP.setOrbitType(type);
    NP.setInitialState(iSR);
    PVCoordinatesProvider sun = CelestialBodyFactory.getSun();
    // creation of the force model
    OneAxisEllipsoid earth = new OneAxisEllipsoid(6378136.46, 1.0 / 298.25765, FramesFactory.getITRF(IERSConventions.IERS_2010, true));
    SolarRadiationPressure forceModel = new SolarRadiationPressure(sun, earth.getEquatorialRadius(), new IsotropicRadiationCNES95Convention(500.0, 0.7, 0.7));
    FNP.addForceModel(forceModel);
    NP.addForceModel(forceModel);
    FieldAbsoluteDate<DerivativeStructure> target = J2000.shiftedBy(1000.);
    FieldSpacecraftState<DerivativeStructure> finalState_DS = FNP.propagate(target);
    SpacecraftState finalState_R = NP.propagate(target.toAbsoluteDate());
    FieldPVCoordinates<DerivativeStructure> finPVC_DS = finalState_DS.getPVCoordinates();
    PVCoordinates finPVC_R = finalState_R.getPVCoordinates();
    Assert.assertEquals(0, Vector3D.distance(finPVC_DS.toPVCoordinates().getPosition(), finPVC_R.getPosition()), 4.0e-9);
    long number = 23091991;
    RandomGenerator RG = new Well19937a(number);
    GaussianRandomGenerator NGG = new GaussianRandomGenerator(RG);
    UncorrelatedRandomVectorGenerator URVG = new UncorrelatedRandomVectorGenerator(new double[] { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 }, new double[] { 1e3, 0.01, 0.01, 0.01, 0.01, 0.01 }, NGG);
    double a_R = a_0.getReal();
    double e_R = e_0.getReal();
    double i_R = i_0.getReal();
    double R_R = R_0.getReal();
    double O_R = O_0.getReal();
    double n_R = n_0.getReal();
    for (int ii = 0; ii < 1; ii++) {
        double[] rand_next = URVG.nextVector();
        double a_shift = a_R + rand_next[0];
        double e_shift = e_R + rand_next[1];
        double i_shift = i_R + rand_next[2];
        double R_shift = R_R + rand_next[3];
        double O_shift = O_R + rand_next[4];
        double n_shift = n_R + rand_next[5];
        KeplerianOrbit shiftedOrb = new KeplerianOrbit(a_shift, e_shift, i_shift, R_shift, O_shift, n_shift, PositionAngle.MEAN, EME, J2000.toAbsoluteDate(), Constants.EIGEN5C_EARTH_MU);
        SpacecraftState shift_iSR = new SpacecraftState(shiftedOrb);
        NumericalPropagator shift_NP = new NumericalPropagator(RIntegrator);
        shift_NP.setOrbitType(type);
        shift_NP.setInitialState(shift_iSR);
        shift_NP.addForceModel(forceModel);
        SpacecraftState finalState_shift = shift_NP.propagate(target.toAbsoluteDate());
        PVCoordinates finPVC_shift = finalState_shift.getPVCoordinates();
        // position check
        FieldVector3D<DerivativeStructure> pos_DS = finPVC_DS.getPosition();
        double x_DS = pos_DS.getX().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double y_DS = pos_DS.getY().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double z_DS = pos_DS.getZ().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        // System.out.println(pos_DS.getX().getPartialDerivative(1));
        double x = finPVC_shift.getPosition().getX();
        double y = finPVC_shift.getPosition().getY();
        double z = finPVC_shift.getPosition().getZ();
        Assert.assertEquals(x_DS, x, FastMath.abs(x - pos_DS.getX().getReal()) * 4e-9);
        Assert.assertEquals(y_DS, y, FastMath.abs(y - pos_DS.getY().getReal()) * 5e-9);
        Assert.assertEquals(z_DS, z, FastMath.abs(z - pos_DS.getZ().getReal()) * 6e-10);
        // velocity check
        FieldVector3D<DerivativeStructure> vel_DS = finPVC_DS.getVelocity();
        double vx_DS = vel_DS.getX().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double vy_DS = vel_DS.getY().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double vz_DS = vel_DS.getZ().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double vx = finPVC_shift.getVelocity().getX();
        double vy = finPVC_shift.getVelocity().getY();
        double vz = finPVC_shift.getVelocity().getZ();
        Assert.assertEquals(vx_DS, vx, FastMath.abs(vx) * 5e-11);
        Assert.assertEquals(vy_DS, vy, FastMath.abs(vy) * 3e-10);
        Assert.assertEquals(vz_DS, vz, FastMath.abs(vz) * 5e-11);
        // acceleration check
        FieldVector3D<DerivativeStructure> acc_DS = finPVC_DS.getAcceleration();
        double ax_DS = acc_DS.getX().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double ay_DS = acc_DS.getY().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double az_DS = acc_DS.getZ().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double ax = finPVC_shift.getAcceleration().getX();
        double ay = finPVC_shift.getAcceleration().getY();
        double az = finPVC_shift.getAcceleration().getZ();
        Assert.assertEquals(ax_DS, ax, FastMath.abs(ax) * 2e-10);
        Assert.assertEquals(ay_DS, ay, FastMath.abs(ay) * 4e-10);
        Assert.assertEquals(az_DS, az, FastMath.abs(az) * 7e-10);
    }
}

Example 19 with DormandPrince853FieldIntegrator

use of org.hipparchus.ode.nonstiff.DormandPrince853FieldIntegrator in project Orekit by CS-SI.

the class SolarRadiationPressureTest method RealFieldExpectErrorTest.

/**
 *Same test as the previous one but not adding the ForceModel to the NumericalPropagator
 *    it is a test to validate the previous test.
 *    (to test if the ForceModel it's actually
 *    doing something in the Propagator and the FieldPropagator)
 */
@Test
public void RealFieldExpectErrorTest() throws OrekitException {
    DSFactory factory = new DSFactory(6, 0);
    DerivativeStructure a_0 = factory.variable(0, 7e7);
    DerivativeStructure e_0 = factory.variable(1, 0.4);
    DerivativeStructure i_0 = factory.variable(2, 85 * FastMath.PI / 180);
    DerivativeStructure R_0 = factory.variable(3, 0.7);
    DerivativeStructure O_0 = factory.variable(4, 0.5);
    DerivativeStructure n_0 = factory.variable(5, 0.1);
    Field<DerivativeStructure> field = a_0.getField();
    DerivativeStructure zero = field.getZero();
    FieldAbsoluteDate<DerivativeStructure> J2000 = new FieldAbsoluteDate<>(field);
    Frame EME = FramesFactory.getEME2000();
    FieldKeplerianOrbit<DerivativeStructure> FKO = new FieldKeplerianOrbit<>(a_0, e_0, i_0, R_0, O_0, n_0, PositionAngle.MEAN, EME, J2000, Constants.EIGEN5C_EARTH_MU);
    FieldSpacecraftState<DerivativeStructure> initialState = new FieldSpacecraftState<>(FKO);
    SpacecraftState iSR = initialState.toSpacecraftState();
    final OrbitType type = OrbitType.KEPLERIAN;
    double[][] tolerance = NumericalPropagator.tolerances(0.001, FKO.toOrbit(), type);
    AdaptiveStepsizeFieldIntegrator<DerivativeStructure> integrator = new DormandPrince853FieldIntegrator<>(field, 0.001, 200, tolerance[0], tolerance[1]);
    integrator.setInitialStepSize(zero.add(60));
    AdaptiveStepsizeIntegrator RIntegrator = new DormandPrince853Integrator(0.001, 200, tolerance[0], tolerance[1]);
    RIntegrator.setInitialStepSize(60);
    FieldNumericalPropagator<DerivativeStructure> FNP = new FieldNumericalPropagator<>(field, integrator);
    FNP.setOrbitType(type);
    FNP.setInitialState(initialState);
    NumericalPropagator NP = new NumericalPropagator(RIntegrator);
    NP.setInitialState(iSR);
    PVCoordinatesProvider sun = CelestialBodyFactory.getSun();
    // creation of the force model
    OneAxisEllipsoid earth = new OneAxisEllipsoid(6378136.46, 1.0 / 298.25765, FramesFactory.getITRF(IERSConventions.IERS_2010, true));
    SolarRadiationPressure forceModel = new SolarRadiationPressure(sun, earth.getEquatorialRadius(), new IsotropicRadiationCNES95Convention(500.0, 0.7, 0.7));
    FNP.addForceModel(forceModel);
    // NOT ADDING THE FORCE MODEL TO THE NUMERICAL PROPAGATOR   NP.addForceModel(forceModel);
    FieldAbsoluteDate<DerivativeStructure> target = J2000.shiftedBy(1000.);
    FieldSpacecraftState<DerivativeStructure> finalState_DS = FNP.propagate(target);
    SpacecraftState finalState_R = NP.propagate(target.toAbsoluteDate());
    FieldPVCoordinates<DerivativeStructure> finPVC_DS = finalState_DS.getPVCoordinates();
    PVCoordinates finPVC_R = finalState_R.getPVCoordinates();
    Assert.assertFalse(FastMath.abs(finPVC_DS.toPVCoordinates().getPosition().getX() - finPVC_R.getPosition().getX()) < FastMath.abs(finPVC_R.getPosition().getX()) * 1e-11);
    Assert.assertFalse(FastMath.abs(finPVC_DS.toPVCoordinates().getPosition().getY() - finPVC_R.getPosition().getY()) < FastMath.abs(finPVC_R.getPosition().getY()) * 1e-11);
    Assert.assertFalse(FastMath.abs(finPVC_DS.toPVCoordinates().getPosition().getZ() - finPVC_R.getPosition().getZ()) < FastMath.abs(finPVC_R.getPosition().getZ()) * 1e-11);
}

Example 20 with DormandPrince853FieldIntegrator

use of org.hipparchus.ode.nonstiff.DormandPrince853FieldIntegrator in project Orekit by CS-SI.

the class SolarRadiationPressureTest method RealFieldBoxTest.

/**
 *Testing if the propagation between the FieldPropagation and the propagation
 * is equivalent.
 * Also testing if propagating X+dX with the propagation is equivalent to
 * propagation X with the FieldPropagation and then applying the taylor
 * expansion of dX to the result.
 */
@Test
public void RealFieldBoxTest() throws OrekitException {
    DSFactory factory = new DSFactory(6, 5);
    DerivativeStructure a_0 = factory.variable(0, 7e7);
    DerivativeStructure e_0 = factory.variable(1, 0.4);
    DerivativeStructure i_0 = factory.variable(2, 85 * FastMath.PI / 180);
    DerivativeStructure R_0 = factory.variable(3, 0.7);
    DerivativeStructure O_0 = factory.variable(4, 0.5);
    DerivativeStructure n_0 = factory.variable(5, 0.1);
    Field<DerivativeStructure> field = a_0.getField();
    DerivativeStructure zero = field.getZero();
    FieldAbsoluteDate<DerivativeStructure> J2000 = FieldAbsoluteDate.getJ2000Epoch(field);
    Frame EME = FramesFactory.getEME2000();
    FieldKeplerianOrbit<DerivativeStructure> FKO = new FieldKeplerianOrbit<>(a_0, e_0, i_0, R_0, O_0, n_0, PositionAngle.MEAN, EME, J2000, Constants.EIGEN5C_EARTH_MU);
    FieldSpacecraftState<DerivativeStructure> initialState = new FieldSpacecraftState<>(FKO);
    SpacecraftState iSR = initialState.toSpacecraftState();
    final OrbitType type = OrbitType.KEPLERIAN;
    double[][] tolerance = NumericalPropagator.tolerances(10.0, FKO.toOrbit(), type);
    AdaptiveStepsizeFieldIntegrator<DerivativeStructure> integrator = new DormandPrince853FieldIntegrator<>(field, 0.001, 200, tolerance[0], tolerance[1]);
    integrator.setInitialStepSize(zero.add(60));
    AdaptiveStepsizeIntegrator RIntegrator = new DormandPrince853Integrator(0.001, 200, tolerance[0], tolerance[1]);
    RIntegrator.setInitialStepSize(60);
    FieldNumericalPropagator<DerivativeStructure> FNP = new FieldNumericalPropagator<>(field, integrator);
    FNP.setOrbitType(type);
    FNP.setInitialState(initialState);
    NumericalPropagator NP = new NumericalPropagator(RIntegrator);
    NP.setOrbitType(type);
    NP.setInitialState(iSR);
    PVCoordinatesProvider sun = CelestialBodyFactory.getSun();
    // creation of the force model
    OneAxisEllipsoid earth = new OneAxisEllipsoid(6378136.46, 1.0 / 298.25765, FramesFactory.getITRF(IERSConventions.IERS_2010, true));
    SolarRadiationPressure forceModel = new SolarRadiationPressure(sun, earth.getEquatorialRadius(), new BoxAndSolarArraySpacecraft(1.5, 2.0, 1.8, CelestialBodyFactory.getSun(), 20.0, Vector3D.PLUS_J, initialState.getDate().toAbsoluteDate(), Vector3D.PLUS_K, 1.0e-6, 1.2, 0.7, 0.2));
    FNP.addForceModel(forceModel);
    NP.addForceModel(forceModel);
    NP.setEphemerisMode();
    FieldAbsoluteDate<DerivativeStructure> target = J2000.shiftedBy(1000.);
    FieldSpacecraftState<DerivativeStructure> finalState_DS = FNP.propagate(target);
    SpacecraftState finalState_R = NP.propagate(target.toAbsoluteDate());
    FieldPVCoordinates<DerivativeStructure> finPVC_DS = finalState_DS.getPVCoordinates();
    PVCoordinates finPVC_R = finalState_R.getPVCoordinates();
    Assert.assertEquals(0, Vector3D.distance(finPVC_DS.toPVCoordinates().getPosition(), finPVC_R.getPosition()), 1.0e-8);
    long number = 23091991;
    RandomGenerator RG = new Well19937a(number);
    GaussianRandomGenerator NGG = new GaussianRandomGenerator(RG);
    UncorrelatedRandomVectorGenerator URVG = new UncorrelatedRandomVectorGenerator(new double[] { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 }, new double[] { 1e3, 0.01, 0.01, 0.01, 0.01, 0.01 }, NGG);
    double a_R = a_0.getReal();
    double e_R = e_0.getReal();
    double i_R = i_0.getReal();
    double R_R = R_0.getReal();
    double O_R = O_0.getReal();
    double n_R = n_0.getReal();
    for (int ii = 0; ii < 1; ii++) {
        double[] rand_next = URVG.nextVector();
        double a_shift = a_R + rand_next[0];
        double e_shift = e_R + rand_next[1];
        double i_shift = i_R + rand_next[2];
        double R_shift = R_R + rand_next[3];
        double O_shift = O_R + rand_next[4];
        double n_shift = n_R + rand_next[5];
        KeplerianOrbit shiftedOrb = new KeplerianOrbit(a_shift, e_shift, i_shift, R_shift, O_shift, n_shift, PositionAngle.MEAN, EME, J2000.toAbsoluteDate(), Constants.EIGEN5C_EARTH_MU);
        SpacecraftState shift_iSR = new SpacecraftState(shiftedOrb);
        NumericalPropagator shift_NP = new NumericalPropagator(RIntegrator);
        shift_NP.setInitialState(shift_iSR);
        shift_NP.addForceModel(forceModel);
        SpacecraftState finalState_shift = shift_NP.propagate(target.toAbsoluteDate());
        PVCoordinates finPVC_shift = finalState_shift.getPVCoordinates();
        // position check
        FieldVector3D<DerivativeStructure> pos_DS = finPVC_DS.getPosition();
        double x_DS = pos_DS.getX().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double y_DS = pos_DS.getY().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double z_DS = pos_DS.getZ().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        // System.out.println(pos_DS.getX().getPartialDerivative(1));
        double x = finPVC_shift.getPosition().getX();
        double y = finPVC_shift.getPosition().getY();
        double z = finPVC_shift.getPosition().getZ();
        Assert.assertEquals(x_DS, x, FastMath.abs(x - pos_DS.getX().getReal()) * 4e-9);
        Assert.assertEquals(y_DS, y, FastMath.abs(y - pos_DS.getY().getReal()) * 5e-9);
        Assert.assertEquals(z_DS, z, FastMath.abs(z - pos_DS.getZ().getReal()) * 6e-10);
        // velocity check
        FieldVector3D<DerivativeStructure> vel_DS = finPVC_DS.getVelocity();
        double vx_DS = vel_DS.getX().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double vy_DS = vel_DS.getY().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double vz_DS = vel_DS.getZ().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double vx = finPVC_shift.getVelocity().getX();
        double vy = finPVC_shift.getVelocity().getY();
        double vz = finPVC_shift.getVelocity().getZ();
        Assert.assertEquals(vx_DS, vx, FastMath.abs(vx) * 5e-11);
        Assert.assertEquals(vy_DS, vy, FastMath.abs(vy) * 3e-10);
        Assert.assertEquals(vz_DS, vz, FastMath.abs(vz) * 5e-11);
        // acceleration check
        FieldVector3D<DerivativeStructure> acc_DS = finPVC_DS.getAcceleration();
        double ax_DS = acc_DS.getX().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double ay_DS = acc_DS.getY().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double az_DS = acc_DS.getZ().taylor(rand_next[0], rand_next[1], rand_next[2], rand_next[3], rand_next[4], rand_next[5]);
        double ax = finPVC_shift.getAcceleration().getX();
        double ay = finPVC_shift.getAcceleration().getY();
        double az = finPVC_shift.getAcceleration().getZ();
        Assert.assertEquals(ax_DS, ax, FastMath.abs(ax) * 2e-10);
        Assert.assertEquals(ay_DS, ay, FastMath.abs(ay) * 4e-10);
        Assert.assertEquals(az_DS, az, FastMath.abs(az) * 7e-10);
    }
}