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

Example 1 with DormandPrince853FieldIntegrator

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

the class HarmonicParametricAccelerationTest method doTestEquivalentManeuver.

private <T extends RealFieldElement<T>> void doTestEquivalentManeuver(final Field<T> field, final double mass, final AttitudeProvider maneuverLaw, final ConstantThrustManeuver maneuver, final AttitudeProvider accelerationLaw, final HarmonicParametricAcceleration parametricAcceleration, final double positionTolerance) throws OrekitException {
    FieldSpacecraftState<T> initialState = new FieldSpacecraftState<>(field, new SpacecraftState(initialOrbit, maneuverLaw.getAttitude(initialOrbit, initialOrbit.getDate(), initialOrbit.getFrame()), mass));
    double[][] tolerance = FieldNumericalPropagator.tolerances(field.getZero().add(10), initialState.getOrbit(), initialState.getOrbit().getType());
    // propagator 0 uses a maneuver that is so efficient it does not consume any fuel
    // (hence mass remains constant)
    AdaptiveStepsizeFieldIntegrator<T> integrator0 = new DormandPrince853FieldIntegrator<>(field, 0.001, 100, tolerance[0], tolerance[1]);
    integrator0.setInitialStepSize(field.getZero().add(60));
    final FieldNumericalPropagator<T> propagator0 = new FieldNumericalPropagator<>(field, integrator0);
    propagator0.setInitialState(initialState);
    propagator0.setAttitudeProvider(maneuverLaw);
    propagator0.addForceModel(maneuver);
    propagator0.setEphemerisMode();
    propagator0.propagate(initialState.getDate(), initialState.getDate().shiftedBy(1000.0));
    FieldBoundedPropagator<T> ephemeris0 = propagator0.getGeneratedEphemeris();
    // propagator 1 uses a constant acceleration
    AdaptiveStepsizeFieldIntegrator<T> integrator1 = new DormandPrince853FieldIntegrator<>(field, 0.001, 100, tolerance[0], tolerance[1]);
    integrator1.setInitialStepSize(field.getZero().add(60));
    final FieldNumericalPropagator<T> propagator1 = new FieldNumericalPropagator<>(field, integrator1);
    propagator1.setInitialState(initialState);
    propagator1.setAttitudeProvider(accelerationLaw);
    propagator1.addForceModel(parametricAcceleration);
    propagator1.setEphemerisMode();
    propagator1.propagate(initialState.getDate(), initialState.getDate().shiftedBy(1000.0));
    FieldBoundedPropagator<T> ephemeris1 = propagator1.getGeneratedEphemeris();
    for (double dt = 1; dt < 999; dt += 10) {
        FieldAbsoluteDate<T> t = initialState.getDate().shiftedBy(dt);
        FieldVector3D<T> p0 = ephemeris0.propagate(t).getPVCoordinates().getPosition();
        FieldVector3D<T> p1 = ephemeris1.propagate(t).getPVCoordinates().getPosition();
        Assert.assertEquals(0, FieldVector3D.distance(p0, p1).getReal(), positionTolerance);
    }
}

Example 2 with DormandPrince853FieldIntegrator

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

the class PolynomialParametricAccelerationTest method doTestEquivalentManeuver.

private <T extends RealFieldElement<T>> void doTestEquivalentManeuver(final Field<T> field, final double mass, final AttitudeProvider maneuverLaw, final ConstantThrustManeuver maneuver, final AttitudeProvider accelerationLaw, final PolynomialParametricAcceleration parametricAcceleration, final double positionTolerance) throws OrekitException {
    FieldSpacecraftState<T> initialState = new FieldSpacecraftState<>(field, new SpacecraftState(initialOrbit, maneuverLaw.getAttitude(initialOrbit, initialOrbit.getDate(), initialOrbit.getFrame()), mass));
    double[][] tolerance = FieldNumericalPropagator.tolerances(field.getZero().add(10), initialState.getOrbit(), initialState.getOrbit().getType());
    // propagator 0 uses a maneuver that is so efficient it does not consume any fuel
    // (hence mass remains constant)
    AdaptiveStepsizeFieldIntegrator<T> integrator0 = new DormandPrince853FieldIntegrator<>(field, 0.001, 100, tolerance[0], tolerance[1]);
    integrator0.setInitialStepSize(field.getZero().add(60));
    final FieldNumericalPropagator<T> propagator0 = new FieldNumericalPropagator<>(field, integrator0);
    propagator0.setInitialState(initialState);
    propagator0.setAttitudeProvider(maneuverLaw);
    propagator0.addForceModel(maneuver);
    propagator0.setEphemerisMode();
    propagator0.propagate(initialState.getDate(), initialState.getDate().shiftedBy(1000.0));
    FieldBoundedPropagator<T> ephemeris0 = propagator0.getGeneratedEphemeris();
    // propagator 1 uses a constant acceleration
    AdaptiveStepsizeFieldIntegrator<T> integrator1 = new DormandPrince853FieldIntegrator<>(field, 0.001, 100, tolerance[0], tolerance[1]);
    integrator1.setInitialStepSize(field.getZero().add(60));
    final FieldNumericalPropagator<T> propagator1 = new FieldNumericalPropagator<>(field, integrator1);
    propagator1.setInitialState(initialState);
    propagator1.setAttitudeProvider(accelerationLaw);
    propagator1.addForceModel(parametricAcceleration);
    propagator1.setEphemerisMode();
    propagator1.propagate(initialState.getDate(), initialState.getDate().shiftedBy(1000.0));
    FieldBoundedPropagator<T> ephemeris1 = propagator1.getGeneratedEphemeris();
    for (double dt = 1; dt < 999; dt += 10) {
        FieldAbsoluteDate<T> t = initialState.getDate().shiftedBy(dt);
        FieldVector3D<T> p0 = ephemeris0.propagate(t).getPVCoordinates().getPosition();
        FieldVector3D<T> p1 = ephemeris1.propagate(t).getPVCoordinates().getPosition();
        Assert.assertEquals(0, FieldVector3D.distance(p0, p1).getReal(), positionTolerance);
    }
}

Example 3 with DormandPrince853FieldIntegrator

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

the class DragForceTest 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, 5);
    DerivativeStructure a_0 = factory.variable(0, 7e6);
    DerivativeStructure e_0 = factory.variable(1, 0.01);
    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();
    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);
    final DragForce forceModel = new DragForce(new HarrisPriester(CelestialBodyFactory.getSun(), new OneAxisEllipsoid(Constants.WGS84_EARTH_EQUATORIAL_RADIUS, Constants.WGS84_EARTH_FLATTENING, FramesFactory.getITRF(IERSConventions.IERS_2010, true))), new BoxAndSolarArraySpacecraft(1.5, 2.0, 1.8, CelestialBodyFactory.getSun(), 20.0, Vector3D.PLUS_J, 1.2, 0.7, 0.2));
    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 4 with DormandPrince853FieldIntegrator

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

the class HolmesFeatherstoneAttractionModelTest method RealFieldTest.

/**
 *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 RealFieldTest() throws OrekitException {
    DSFactory factory = new DSFactory(6, 4);
    DerivativeStructure a_0 = factory.variable(0, 7201009.7124401);
    DerivativeStructure e_0 = factory.variable(1, 1e-3);
    DerivativeStructure i_0 = factory.variable(2, 98.7 * FastMath.PI / 180);
    DerivativeStructure R_0 = factory.variable(3, 15.0 * 22.5 * FastMath.PI / 180);
    DerivativeStructure O_0 = factory.variable(4, 93.0 * FastMath.PI / 180);
    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();
    OrbitType type = OrbitType.EQUINOCTIAL;
    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);
    double[][] c = new double[3][1];
    c[0][0] = 0.0;
    c[2][0] = normalizedC20;
    double[][] s = new double[3][1];
    NormalizedSphericalHarmonicsProvider provider = GravityFieldFactory.getNormalizedProvider(6378136.460, mu, TideSystem.UNKNOWN, c, s);
    HolmesFeatherstoneAttractionModel forceModel = new HolmesFeatherstoneAttractionModel(itrf, provider);
    FNP.addForceModel(forceModel);
    NP.addForceModel(forceModel);
    FieldAbsoluteDate<DerivativeStructure> target = J2000.shiftedBy(1005.);
    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(finPVC_DS.toPVCoordinates().getPosition().getX(), finPVC_R.getPosition().getX(), FastMath.abs(finPVC_R.getPosition().getX()) * 1e-11);
    Assert.assertEquals(finPVC_DS.toPVCoordinates().getPosition().getY(), finPVC_R.getPosition().getY(), FastMath.abs(finPVC_R.getPosition().getY()) * 1e-11);
    Assert.assertEquals(finPVC_DS.toPVCoordinates().getPosition().getZ(), finPVC_R.getPosition().getZ(), FastMath.abs(finPVC_R.getPosition().getZ()) * 1e-11);
    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[] { 1e1, 0.001, 0.001, 0.001, 0.001, 0.001 }, 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]);
        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()) * 1e-8);
        Assert.assertEquals(y_DS, y, FastMath.abs(y - pos_DS.getY().getReal()) * 1e-8);
        Assert.assertEquals(z_DS, z, FastMath.abs(z - pos_DS.getZ().getReal()) * 1e-8);
        // 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) * 1e-9);
        Assert.assertEquals(vy_DS, vy, FastMath.abs(vy) * 1e-9);
        Assert.assertEquals(vz_DS, vz, FastMath.abs(vz) * 1e-9);
        // 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) * 1e-9);
        Assert.assertEquals(ay_DS, ay, FastMath.abs(ay) * 1e-9);
        Assert.assertEquals(az_DS, az, FastMath.abs(az) * 1e-9);
    }
}

Example 5 with DormandPrince853FieldIntegrator

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

the class FieldNumericalPropagatorTest method doTestPropagationTypesElliptical.

private <T extends RealFieldElement<T>> void doTestPropagationTypesElliptical(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);
    ForceModel gravityField = new HolmesFeatherstoneAttractionModel(FramesFactory.getITRF(IERSConventions.IERS_2010, true), GravityFieldFactory.getNormalizedProvider(5, 5));
    propagator.addForceModel(gravityField);
    // Propagation of the initial at t + dt
    final FieldPVCoordinates<T> pv = initialState.getPVCoordinates();
    final T dP = zero.add(0.001);
    final T dV = pv.getPosition().getNormSq().multiply(pv.getVelocity().getNorm()).reciprocal().multiply(dP.multiply(initialState.getMu()));
    final FieldPVCoordinates<T> pvcM = propagateInType(initialState, dP, OrbitType.CARTESIAN, PositionAngle.MEAN, propagator);
    final FieldPVCoordinates<T> pviM = propagateInType(initialState, dP, OrbitType.CIRCULAR, PositionAngle.MEAN, propagator);
    final FieldPVCoordinates<T> pveM = propagateInType(initialState, dP, OrbitType.EQUINOCTIAL, PositionAngle.MEAN, propagator);
    final FieldPVCoordinates<T> pvkM = propagateInType(initialState, dP, OrbitType.KEPLERIAN, PositionAngle.MEAN, propagator);
    final FieldPVCoordinates<T> pvcE = propagateInType(initialState, dP, OrbitType.CARTESIAN, PositionAngle.ECCENTRIC, propagator);
    final FieldPVCoordinates<T> pviE = propagateInType(initialState, dP, OrbitType.CIRCULAR, PositionAngle.ECCENTRIC, propagator);
    final FieldPVCoordinates<T> pveE = propagateInType(initialState, dP, OrbitType.EQUINOCTIAL, PositionAngle.ECCENTRIC, propagator);
    final FieldPVCoordinates<T> pvkE = propagateInType(initialState, dP, OrbitType.KEPLERIAN, PositionAngle.ECCENTRIC, propagator);
    final FieldPVCoordinates<T> pvcT = propagateInType(initialState, dP, OrbitType.CARTESIAN, PositionAngle.TRUE, propagator);
    final FieldPVCoordinates<T> pviT = propagateInType(initialState, dP, OrbitType.CIRCULAR, PositionAngle.TRUE, propagator);
    final FieldPVCoordinates<T> pveT = propagateInType(initialState, dP, OrbitType.EQUINOCTIAL, PositionAngle.TRUE, propagator);
    final FieldPVCoordinates<T> pvkT = propagateInType(initialState, dP, OrbitType.KEPLERIAN, PositionAngle.TRUE, propagator);
    Assert.assertEquals(0, pvcM.getPosition().subtract(pveT.getPosition()).getNorm().getReal() / dP.getReal(), 3.0);
    Assert.assertEquals(0, pvcM.getVelocity().subtract(pveT.getVelocity()).getNorm().getReal() / dV.getReal(), 2.0);
    Assert.assertEquals(0, pviM.getPosition().subtract(pveT.getPosition()).getNorm().getReal() / dP.getReal(), 0.6);
    Assert.assertEquals(0, pviM.getVelocity().subtract(pveT.getVelocity()).getNorm().getReal() / dV.getReal(), 0.4);
    Assert.assertEquals(0, pvkM.getPosition().subtract(pveT.getPosition()).getNorm().getReal() / dP.getReal(), 0.5);
    Assert.assertEquals(0, pvkM.getVelocity().subtract(pveT.getVelocity()).getNorm().getReal() / dV.getReal(), 0.3);
    Assert.assertEquals(0, pveM.getPosition().subtract(pveT.getPosition()).getNorm().getReal() / dP.getReal(), 0.2);
    Assert.assertEquals(0, pveM.getVelocity().subtract(pveT.getVelocity()).getNorm().getReal() / dV.getReal(), 0.2);
    Assert.assertEquals(0, pvcE.getPosition().subtract(pveT.getPosition()).getNorm().getReal() / dP.getReal(), 3.0);
    Assert.assertEquals(0, pvcE.getVelocity().subtract(pveT.getVelocity()).getNorm().getReal() / dV.getReal(), 2.0);
    Assert.assertEquals(0, pviE.getPosition().subtract(pveT.getPosition()).getNorm().getReal() / dP.getReal(), 0.03);
    Assert.assertEquals(0, pviE.getVelocity().subtract(pveT.getVelocity()).getNorm().getReal() / dV.getReal(), 0.04);
    Assert.assertEquals(0, pvkE.getPosition().subtract(pveT.getPosition()).getNorm().getReal() / dP.getReal(), 0.4);
    Assert.assertEquals(0, pvkE.getVelocity().subtract(pveT.getVelocity()).getNorm().getReal() / dV.getReal(), 0.3);
    Assert.assertEquals(0, pveE.getPosition().subtract(pveT.getPosition()).getNorm().getReal() / dP.getReal(), 0.2);
    Assert.assertEquals(0, pveE.getVelocity().subtract(pveT.getVelocity()).getNorm().getReal() / dV.getReal(), 0.07);
    Assert.assertEquals(0, pvcT.getPosition().subtract(pveT.getPosition()).getNorm().getReal() / dP.getReal(), 3.0);
    Assert.assertEquals(0, pvcT.getVelocity().subtract(pveT.getVelocity()).getNorm().getReal() / dV.getReal(), 2.0);
    Assert.assertEquals(0, pviT.getPosition().subtract(pveT.getPosition()).getNorm().getReal() / dP.getReal(), 0.3);
    Assert.assertEquals(0, pviT.getVelocity().subtract(pveT.getVelocity()).getNorm().getReal() / dV.getReal(), 0.2);
    Assert.assertEquals(0, pvkT.getPosition().subtract(pveT.getPosition()).getNorm().getReal() / dP.getReal(), 0.4);
    Assert.assertEquals(0, pvkT.getVelocity().subtract(pveT.getVelocity()).getNorm().getReal() / dV.getReal(), 0.2);
}