/* Copyright 2002-2017 CS Systèmes d'Information
* Licensed to CS Systèmes d'Information (CS) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* CS licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.orekit.utils;
import java.lang.reflect.InvocationTargetException;
import java.lang.reflect.Method;
import org.hipparchus.exception.MathIllegalArgumentException;
import org.hipparchus.geometry.euclidean.threed.Rotation;
import org.hipparchus.geometry.euclidean.threed.RotationConvention;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.ode.ODEIntegrator;
import org.hipparchus.ode.ODEState;
import org.hipparchus.ode.ODEStateAndDerivative;
import org.hipparchus.ode.OrdinaryDifferentialEquation;
import org.hipparchus.ode.nonstiff.DormandPrince853Integrator;
import org.hipparchus.ode.sampling.ODEFixedStepHandler;
import org.hipparchus.ode.sampling.StepNormalizer;
import org.hipparchus.random.RandomGenerator;
import org.hipparchus.random.Well1024a;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;
import org.hipparchus.util.Precision;
import org.junit.Assert;
import org.junit.Test;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitMessages;
public class AngularCoordinatesTest {
@Test
public void testDefaultConstructor() throws OrekitException {
AngularCoordinates ac = new AngularCoordinates();
Assert.assertEquals(0.0, ac.getRotationAcceleration().getNorm(), 1.0e-15);
Assert.assertEquals(0.0, ac.getRotationRate().getNorm(), 1.0e-15);
Assert.assertEquals(0.0, Rotation.distance(ac.getRotation(), Rotation.IDENTITY), 1.0e-10);
}
@Test
public void testDerivativesStructuresNeg() throws OrekitException {
try {
AngularCoordinates.IDENTITY.toDerivativeStructureRotation(-1);
Assert.fail("an exception should have been thrown");
} catch (OrekitException oe) {
Assert.assertEquals(OrekitMessages.OUT_OF_RANGE_DERIVATION_ORDER, oe.getSpecifier());
Assert.assertEquals(-1, ((Integer) (oe.getParts()[0])).intValue());
}
}
@Test
public void testDerivativesStructures3() throws OrekitException {
try {
AngularCoordinates.IDENTITY.toDerivativeStructureRotation(3);
Assert.fail("an exception should have been thrown");
} catch (OrekitException oe) {
Assert.assertEquals(OrekitMessages.OUT_OF_RANGE_DERIVATION_ORDER, oe.getSpecifier());
Assert.assertEquals(3, ((Integer) (oe.getParts()[0])).intValue());
}
}
@Test
public void testDerivativesStructures0() throws OrekitException {
RandomGenerator random = new Well1024a(0x18a0a08fd63f047al);
Rotation r = randomRotation(random);
Vector3D o = randomVector(random, 1.0e-2);
Vector3D oDot = randomVector(random, 1.0e-2);
AngularCoordinates ac = new AngularCoordinates(r, o, oDot);
AngularCoordinates rebuilt = new AngularCoordinates(ac.toDerivativeStructureRotation(0));
Assert.assertEquals(0.0, Rotation.distance(ac.getRotation(), rebuilt.getRotation()), 1.0e-15);
Assert.assertEquals(0.0, rebuilt.getRotationRate().getNorm(), 1.0e-15);
Assert.assertEquals(0.0, rebuilt.getRotationAcceleration().getNorm(), 1.0e-15);
}
@Test
public void testDerivativesStructures1() throws OrekitException {
RandomGenerator random = new Well1024a(0x8f8fc6d27bbdc46dl);
Rotation r = randomRotation(random);
Vector3D o = randomVector(random, 1.0e-2);
Vector3D oDot = randomVector(random, 1.0e-2);
AngularCoordinates ac = new AngularCoordinates(r, o, oDot);
AngularCoordinates rebuilt = new AngularCoordinates(ac.toDerivativeStructureRotation(1));
Assert.assertEquals(0.0, Rotation.distance(ac.getRotation(), rebuilt.getRotation()), 1.0e-15);
Assert.assertEquals(0.0, Vector3D.distance(ac.getRotationRate(), rebuilt.getRotationRate()), 1.0e-15);
Assert.assertEquals(0.0, rebuilt.getRotationAcceleration().getNorm(), 1.0e-15);
}
@Test
public void testDerivativesStructures2() throws OrekitException {
RandomGenerator random = new Well1024a(0x1633878dddac047dl);
Rotation r = randomRotation(random);
Vector3D o = randomVector(random, 1.0e-2);
Vector3D oDot = randomVector(random, 1.0e-2);
AngularCoordinates ac = new AngularCoordinates(r, o, oDot);
AngularCoordinates rebuilt = new AngularCoordinates(ac.toDerivativeStructureRotation(2));
Assert.assertEquals(0.0, Rotation.distance(ac.getRotation(), rebuilt.getRotation()), 1.0e-15);
Assert.assertEquals(0.0, Vector3D.distance(ac.getRotationRate(), rebuilt.getRotationRate()), 1.0e-15);
Assert.assertEquals(0.0, Vector3D.distance(ac.getRotationAcceleration(), rebuilt.getRotationAcceleration()), 1.0e-15);
}
@Test
public void testZeroRate() throws OrekitException {
AngularCoordinates ac =
new AngularCoordinates(new Rotation(0.48, 0.64, 0.36, 0.48, false), Vector3D.ZERO, Vector3D.ZERO);
Assert.assertEquals(Vector3D.ZERO, ac.getRotationRate());
double dt = 10.0;
AngularCoordinates shifted = ac.shiftedBy(dt);
Assert.assertEquals(Vector3D.ZERO, shifted.getRotationAcceleration());
Assert.assertEquals(Vector3D.ZERO, shifted.getRotationRate());
Assert.assertEquals(0.0, Rotation.distance(ac.getRotation(), shifted.getRotation()), 1.0e-15);
}
@Test
public void testShiftWithoutAcceleration() throws OrekitException {
double rate = 2 * FastMath.PI / (12 * 60);
AngularCoordinates ac =
new AngularCoordinates(Rotation.IDENTITY,
new Vector3D(rate, Vector3D.PLUS_K),
Vector3D.ZERO);
Assert.assertEquals(rate, ac.getRotationRate().getNorm(), 1.0e-10);
double dt = 10.0;
double alpha = rate * dt;
AngularCoordinates shifted = ac.shiftedBy(dt);
Assert.assertEquals(rate, shifted.getRotationRate().getNorm(), 1.0e-10);
Assert.assertEquals(alpha, Rotation.distance(ac.getRotation(), shifted.getRotation()), 1.0e-15);
Vector3D xSat = shifted.getRotation().applyInverseTo(Vector3D.PLUS_I);
Assert.assertEquals(0.0, xSat.subtract(new Vector3D(FastMath.cos(alpha), FastMath.sin(alpha), 0)).getNorm(), 1.0e-15);
Vector3D ySat = shifted.getRotation().applyInverseTo(Vector3D.PLUS_J);
Assert.assertEquals(0.0, ySat.subtract(new Vector3D(-FastMath.sin(alpha), FastMath.cos(alpha), 0)).getNorm(), 1.0e-15);
Vector3D zSat = shifted.getRotation().applyInverseTo(Vector3D.PLUS_K);
Assert.assertEquals(0.0, zSat.subtract(Vector3D.PLUS_K).getNorm(), 1.0e-15);
}
@Test
public void testShiftWithAcceleration() throws OrekitException {
double rate = 2 * FastMath.PI / (12 * 60);
double acc = 0.001;
double dt = 1.0;
int n = 2000;
final AngularCoordinates quadratic =
new AngularCoordinates(Rotation.IDENTITY,
new Vector3D(rate, Vector3D.PLUS_K),
new Vector3D(acc, Vector3D.PLUS_J));
final AngularCoordinates linear =
new AngularCoordinates(quadratic.getRotation(), quadratic.getRotationRate(), Vector3D.ZERO);
final OrdinaryDifferentialEquation ode = new OrdinaryDifferentialEquation() {
public int getDimension() {
return 4;
}
public double[] computeDerivatives(final double t, final double[] q) {
final double omegaX = quadratic.getRotationRate().getX() + t * quadratic.getRotationAcceleration().getX();
final double omegaY = quadratic.getRotationRate().getY() + t * quadratic.getRotationAcceleration().getY();
final double omegaZ = quadratic.getRotationRate().getZ() + t * quadratic.getRotationAcceleration().getZ();
return new double[] {
0.5 * MathArrays.linearCombination(-q[1], omegaX, -q[2], omegaY, -q[3], omegaZ),
0.5 * MathArrays.linearCombination( q[0], omegaX, -q[3], omegaY, q[2], omegaZ),
0.5 * MathArrays.linearCombination( q[3], omegaX, q[0], omegaY, -q[1], omegaZ),
0.5 * MathArrays.linearCombination(-q[2], omegaX, q[1], omegaY, q[0], omegaZ)
};
}
};
ODEIntegrator integrator = new DormandPrince853Integrator(1.0e-6, 1.0, 1.0e-12, 1.0e-12);
integrator.addStepHandler(new StepNormalizer(dt / n, new ODEFixedStepHandler() {
public void handleStep(ODEStateAndDerivative s, boolean isLast) {
final double t = s.getTime();
final double[] y = s.getPrimaryState();
Rotation reference = new Rotation(y[0], y[1], y[2], y[3], true);
// the error in shiftedBy taking acceleration into account is cubic
double expectedCubicError = 1.4544e-6 * t * t * t;
Assert.assertEquals(expectedCubicError,
Rotation.distance(reference, quadratic.shiftedBy(t).getRotation()),
0.0001 * expectedCubicError);
// the error in shiftedBy not taking acceleration into account is quadratic
double expectedQuadraticError = 5.0e-4 * t * t;
Assert.assertEquals(expectedQuadraticError,
Rotation.distance(reference, linear.shiftedBy(t).getRotation()),
0.00001 * expectedQuadraticError);
}
}));
double[] y = new double[] {
quadratic.getRotation().getQ0(),
quadratic.getRotation().getQ1(),
quadratic.getRotation().getQ2(),
quadratic.getRotation().getQ3()
};
integrator.integrate(ode, new ODEState(0, y), dt);
}
@Test
public void testSpin() throws OrekitException {
double rate = 2 * FastMath.PI / (12 * 60);
AngularCoordinates angularCoordinates =
new AngularCoordinates(new Rotation(0.48, 0.64, 0.36, 0.48, false),
new Vector3D(rate, Vector3D.PLUS_K));
Assert.assertEquals(rate, angularCoordinates.getRotationRate().getNorm(), 1.0e-10);
double dt = 10.0;
AngularCoordinates shifted = angularCoordinates.shiftedBy(dt);
Assert.assertEquals(rate, shifted.getRotationRate().getNorm(), 1.0e-10);
Assert.assertEquals(rate * dt, Rotation.distance(angularCoordinates.getRotation(), shifted.getRotation()), 1.0e-10);
Vector3D shiftedX = shifted.getRotation().applyInverseTo(Vector3D.PLUS_I);
Vector3D shiftedY = shifted.getRotation().applyInverseTo(Vector3D.PLUS_J);
Vector3D shiftedZ = shifted.getRotation().applyInverseTo(Vector3D.PLUS_K);
Vector3D originalX = angularCoordinates.getRotation().applyInverseTo(Vector3D.PLUS_I);
Vector3D originalY = angularCoordinates.getRotation().applyInverseTo(Vector3D.PLUS_J);
Vector3D originalZ = angularCoordinates.getRotation().applyInverseTo(Vector3D.PLUS_K);
Assert.assertEquals( FastMath.cos(rate * dt), Vector3D.dotProduct(shiftedX, originalX), 1.0e-10);
Assert.assertEquals( FastMath.sin(rate * dt), Vector3D.dotProduct(shiftedX, originalY), 1.0e-10);
Assert.assertEquals( 0.0, Vector3D.dotProduct(shiftedX, originalZ), 1.0e-10);
Assert.assertEquals(-FastMath.sin(rate * dt), Vector3D.dotProduct(shiftedY, originalX), 1.0e-10);
Assert.assertEquals( FastMath.cos(rate * dt), Vector3D.dotProduct(shiftedY, originalY), 1.0e-10);
Assert.assertEquals( 0.0, Vector3D.dotProduct(shiftedY, originalZ), 1.0e-10);
Assert.assertEquals( 0.0, Vector3D.dotProduct(shiftedZ, originalX), 1.0e-10);
Assert.assertEquals( 0.0, Vector3D.dotProduct(shiftedZ, originalY), 1.0e-10);
Assert.assertEquals( 1.0, Vector3D.dotProduct(shiftedZ, originalZ), 1.0e-10);
Vector3D forward = AngularCoordinates.estimateRate(angularCoordinates.getRotation(), shifted.getRotation(), dt);
Assert.assertEquals(0.0, forward.subtract(angularCoordinates.getRotationRate()).getNorm(), 1.0e-10);
Vector3D reversed = AngularCoordinates.estimateRate(shifted.getRotation(), angularCoordinates.getRotation(), dt);
Assert.assertEquals(0.0, reversed.add(angularCoordinates.getRotationRate()).getNorm(), 1.0e-10);
}
@Test
public void testReverseOffset() {
RandomGenerator random = new Well1024a(0x4ecca9d57a8f1611l);
for (int i = 0; i < 100; ++i) {
Rotation r = randomRotation(random);
Vector3D o = randomVector(random, 1.0e-3);
AngularCoordinates ac = new AngularCoordinates(r, o);
AngularCoordinates sum = ac.addOffset(ac.revert());
Assert.assertEquals(0.0, sum.getRotation().getAngle(), 1.0e-15);
Assert.assertEquals(0.0, sum.getRotationRate().getNorm(), 1.0e-15);
Assert.assertEquals(0.0, sum.getRotationAcceleration().getNorm(), 1.0e-15);
}
}
@Test
public void testNoCommute() {
AngularCoordinates ac1 =
new AngularCoordinates(new Rotation(0.48, 0.64, 0.36, 0.48, false), Vector3D.ZERO);
AngularCoordinates ac2 =
new AngularCoordinates(new Rotation(0.36, -0.48, 0.48, 0.64, false), Vector3D.ZERO);
AngularCoordinates add12 = ac1.addOffset(ac2);
AngularCoordinates add21 = ac2.addOffset(ac1);
// the rotations are really different from each other
Assert.assertEquals(2.574, Rotation.distance(add12.getRotation(), add21.getRotation()), 1.0e-3);
}
@Test
public void testRoundTripNoOp() {
RandomGenerator random = new Well1024a(0x1e610cfe89306669l);
for (int i = 0; i < 100; ++i) {
Rotation r1 = randomRotation(random);
Vector3D o1 = randomVector(random, 1.0e-2);
Vector3D oDot1 = randomVector(random, 1.0e-2);
AngularCoordinates ac1 = new AngularCoordinates(r1, o1, oDot1);
Rotation r2 = randomRotation(random);
Vector3D o2 = randomVector(random, 1.0e-2);
Vector3D oDot2 = randomVector(random, 1.0e-2);
AngularCoordinates ac2 = new AngularCoordinates(r2, o2, oDot2);
AngularCoordinates roundTripSA = ac1.subtractOffset(ac2).addOffset(ac2);
Assert.assertEquals(0.0, Rotation.distance(ac1.getRotation(), roundTripSA.getRotation()), 5.0e-16);
Assert.assertEquals(0.0, Vector3D.distance(ac1.getRotationRate(), roundTripSA.getRotationRate()), 2.0e-17);
Assert.assertEquals(0.0, Vector3D.distance(ac1.getRotationAcceleration(), roundTripSA.getRotationAcceleration()), 2.0e-17);
AngularCoordinates roundTripAS = ac1.addOffset(ac2).subtractOffset(ac2);
Assert.assertEquals(0.0, Rotation.distance(ac1.getRotation(), roundTripAS.getRotation()), 5.0e-16);
Assert.assertEquals(0.0, Vector3D.distance(ac1.getRotationRate(), roundTripAS.getRotationRate()), 2.0e-17);
Assert.assertEquals(0.0, Vector3D.distance(ac1.getRotationAcceleration(), roundTripAS.getRotationAcceleration()), 2.0e-17);
}
}
@Test
public void testRodriguesSymmetry() {
// check the two-way conversion result in identity
RandomGenerator random = new Well1024a(0xb1e615aaa8236b52l);
for (int i = 0; i < 1000; ++i) {
Rotation rotation = randomRotation(random);
Vector3D rotationRate = randomVector(random, 0.01);
Vector3D rotationAcceleration = randomVector(random, 0.01);
AngularCoordinates ac = new AngularCoordinates(rotation, rotationRate, rotationAcceleration);
AngularCoordinates rebuilt = AngularCoordinates.createFromModifiedRodrigues(ac.getModifiedRodrigues(1.0));
Assert.assertEquals(0.0, Rotation.distance(rotation, rebuilt.getRotation()), 1.0e-14);
Assert.assertEquals(0.0, Vector3D.distance(rotationRate, rebuilt.getRotationRate()), 1.0e-15);
Assert.assertEquals(0.0, Vector3D.distance(rotationAcceleration, rebuilt.getRotationAcceleration()), 1.0e-15);
}
}
@Test
public void testRodriguesSpecialCases() {
// identity
double[][] identity = new AngularCoordinates(Rotation.IDENTITY, Vector3D.ZERO, Vector3D.ZERO).getModifiedRodrigues(1.0);
for (double[] row : identity) {
for (double element : row) {
Assert.assertEquals(0.0, element, Precision.SAFE_MIN);
}
}
AngularCoordinates acId = AngularCoordinates.createFromModifiedRodrigues(identity);
Assert.assertEquals(0.0, acId.getRotation().getAngle(), Precision.SAFE_MIN);
Assert.assertEquals(0.0, acId.getRotationRate().getNorm(), Precision.SAFE_MIN);
// PI angle rotation (which is singular for non-modified Rodrigues vector)
RandomGenerator random = new Well1024a(0x2158523e6accb859l);
for (int i = 0; i < 100; ++i) {
Vector3D axis = randomVector(random, 1.0);
AngularCoordinates original = new AngularCoordinates(new Rotation(axis, FastMath.PI, RotationConvention.VECTOR_OPERATOR),
Vector3D.ZERO, Vector3D.ZERO);
AngularCoordinates rebuilt = AngularCoordinates.createFromModifiedRodrigues(original.getModifiedRodrigues(1.0));
Assert.assertEquals(FastMath.PI, rebuilt.getRotation().getAngle(), 1.0e-15);
Assert.assertEquals(0.0, FastMath.sin(Vector3D.angle(axis, rebuilt.getRotation().getAxis(RotationConvention.VECTOR_OPERATOR))), 1.0e-15);
Assert.assertEquals(0.0, rebuilt.getRotationRate().getNorm(), 1.0e-16);
}
}
@Test
public void testInverseCrossProducts()
throws OrekitException {
checkInverse(Vector3D.PLUS_K, Vector3D.PLUS_I, Vector3D.PLUS_J);
checkInverse(Vector3D.ZERO, Vector3D.ZERO, Vector3D.ZERO);
checkInverse(Vector3D.ZERO, Vector3D.ZERO, Vector3D.PLUS_J);
checkInverse(Vector3D.PLUS_K, Vector3D.PLUS_K, Vector3D.PLUS_J);
checkInverse(Vector3D.ZERO, Vector3D.PLUS_K, Vector3D.ZERO);
checkInverse(Vector3D.PLUS_K, Vector3D.PLUS_I, Vector3D.PLUS_K);
checkInverse(Vector3D.PLUS_K, Vector3D.PLUS_I, Vector3D.PLUS_I);
checkInverse(Vector3D.PLUS_K, Vector3D.PLUS_I, new Vector3D(1, 0, -1).normalize());
checkInverse(Vector3D.ZERO, Vector3D.PLUS_I, Vector3D.ZERO, Vector3D.PLUS_J, Vector3D.ZERO);
}
@Test
public void testInverseCrossProductsFailures() {
checkInverseFailure(Vector3D.PLUS_K, Vector3D.ZERO, Vector3D.PLUS_J, Vector3D.PLUS_I, Vector3D.PLUS_K);
checkInverseFailure(Vector3D.PLUS_K, Vector3D.ZERO, Vector3D.ZERO, Vector3D.ZERO, Vector3D.PLUS_K);
checkInverseFailure(Vector3D.PLUS_I, Vector3D.PLUS_I, Vector3D.ZERO, Vector3D.MINUS_I, Vector3D.PLUS_K);
checkInverseFailure(Vector3D.PLUS_I, Vector3D.PLUS_I, Vector3D.ZERO, Vector3D.PLUS_J, Vector3D.PLUS_J);
checkInverseFailure(Vector3D.PLUS_I, Vector3D.PLUS_I, Vector3D.PLUS_J, Vector3D.PLUS_J, Vector3D.ZERO);
checkInverseFailure(Vector3D.PLUS_I, Vector3D.PLUS_I, Vector3D.PLUS_J, Vector3D.ZERO, Vector3D.PLUS_J);
}
@Test
public void testRandomInverseCrossProducts() throws OrekitException {
RandomGenerator generator = new Well1024a(0x52b29d8f6ac2d64bl);
for (int i = 0; i < 10000; ++i) {
Vector3D omega = randomVector(generator, 10 * generator.nextDouble() + 1.0);
Vector3D v1 = randomVector(generator, 10 * generator.nextDouble() + 1.0);
Vector3D v2 = randomVector(generator, 10 * generator.nextDouble() + 1.0);
checkInverse(omega, v1, v2);
}
}
private void checkInverse(Vector3D omega, Vector3D v1, Vector3D v2) throws OrekitException {
checkInverse(omega,
v1, Vector3D.crossProduct(omega, v1),
v2, Vector3D.crossProduct(omega, v2));
}
private void checkInverseFailure(Vector3D omega, Vector3D v1, Vector3D c1, Vector3D v2, Vector3D c2) {
try {
checkInverse(omega, v1, c1, v2, c2);
Assert.fail("an exception should have been thrown");
} catch (MathIllegalArgumentException miae) {
// expected
}
}
private void checkInverse(Vector3D omega, Vector3D v1, Vector3D c1, Vector3D v2, Vector3D c2)
throws MathIllegalArgumentException {
try {
Method inverse;
inverse = AngularCoordinates.class.getDeclaredMethod("inverseCrossProducts",
Vector3D.class, Vector3D.class,
Vector3D.class, Vector3D.class,
double.class);
inverse.setAccessible(true);
Vector3D rebuilt = (Vector3D) inverse.invoke(null, v1, c1, v2, c2, 1.0e-9);
Assert.assertEquals(0.0, Vector3D.distance(omega, rebuilt), 5.0e-12 * omega.getNorm());
} catch (NoSuchMethodException e) {
Assert.fail(e.getLocalizedMessage());
} catch (SecurityException e) {
Assert.fail(e.getLocalizedMessage());
} catch (IllegalAccessException e) {
Assert.fail(e.getLocalizedMessage());
} catch (IllegalArgumentException e) {
Assert.fail(e.getLocalizedMessage());
} catch (InvocationTargetException e) {
throw (MathIllegalArgumentException) e.getCause();
}
}
@Test
public void testRandomPVCoordinates() throws OrekitException {
RandomGenerator generator = new Well1024a(0x49eb5b92d1f94b89l);
for (int i = 0; i < 100; ++i) {
Rotation r = randomRotation(generator);
Vector3D omega = randomVector(generator, 10 * generator.nextDouble() + 1.0);
Vector3D omegaDot = randomVector(generator, 0.1 * generator.nextDouble() + 0.01);
AngularCoordinates ref = new AngularCoordinates(r, omega, omegaDot);
AngularCoordinates inv = ref.revert();
for (int j = 0; j < 100; ++j) {
PVCoordinates v1 = randomPVCoordinates(generator, 1000, 1.0, 0.001);
PVCoordinates v2 = randomPVCoordinates(generator, 1000, 1.0, 0.0010);
PVCoordinates u1 = inv.applyTo(v1);
PVCoordinates u2 = inv.applyTo(v2);
AngularCoordinates rebuilt = new AngularCoordinates(u1, u2, v1, v2, 1.0e-9);
Assert.assertEquals(0.0,
Rotation.distance(r, rebuilt.getRotation()),
4.0e-14);
Assert.assertEquals(0.0,
Vector3D.distance(omega, rebuilt.getRotationRate()),
3.0e-12 * omega.getNorm());
Assert.assertEquals(0.0,
Vector3D.distance(omegaDot, rebuilt.getRotationAcceleration()),
2.0e-6 * omegaDot.getNorm());
}
}
}
@Test
public void testCancellingDerivatives() throws OrekitException {
PVCoordinates u1 = new PVCoordinates(new Vector3D(-0.4466591282528639, -0.009657376949231283, -0.894652087807798),
new Vector3D(-8.897296517803556E-4, 2.7825250920407674E-4, 4.411979658413134E-4),
new Vector3D( 4.753127475302486E-7, 1.0209400376727623E-8, 9.515403756524403E-7));
PVCoordinates u2 = new PVCoordinates(new Vector3D( 0.23723907259910096, 0.9628700806685033, -0.1288364474275361),
new Vector3D(-7.98741002062555E-24, 2.4979687659429984E-24, 3.9607863426704016E-24),
new Vector3D(-3.150541868418562E-23, 9.856329862034835E-24, 1.5648124883326986E-23));
PVCoordinates v1 = new PVCoordinates(Vector3D.PLUS_K, Vector3D.ZERO, Vector3D.ZERO);
PVCoordinates v2 = new PVCoordinates(Vector3D.MINUS_J, Vector3D.ZERO, Vector3D.ZERO);
AngularCoordinates ac = new AngularCoordinates(u1, u2, v1, v2, 1.0e-9);
PVCoordinates v1Computed = ac.applyTo(u1);
PVCoordinates v2Computed = ac.applyTo(u2);
Assert.assertEquals(0, Vector3D.distance(v1.getPosition(), v1Computed.getPosition()), 1.0e-15);
Assert.assertEquals(0, Vector3D.distance(v2.getPosition(), v2Computed.getPosition()), 1.0e-15);
Assert.assertEquals(0, Vector3D.distance(v1.getVelocity(), v1Computed.getVelocity()), 1.0e-15);
Assert.assertEquals(0, Vector3D.distance(v2.getVelocity(), v2Computed.getVelocity()), 1.0e-15);
Assert.assertEquals(0, Vector3D.distance(v1.getAcceleration(), v1Computed.getAcceleration()), 1.0e-15);
Assert.assertEquals(0, Vector3D.distance(v2.getAcceleration(), v2Computed.getAcceleration()), 1.0e-15);
}
private Vector3D randomVector(RandomGenerator random, double norm) {
double n = random.nextDouble() * norm;
double x = random.nextDouble();
double y = random.nextDouble();
double z = random.nextDouble();
return new Vector3D(n, new Vector3D(x, y, z).normalize());
}
private PVCoordinates randomPVCoordinates(RandomGenerator random,
double norm0, double norm1, double norm2) {
Vector3D p0 = randomVector(random, norm0);
Vector3D p1 = randomVector(random, norm1);
Vector3D p2 = randomVector(random, norm2);
return new PVCoordinates(p0, p1, p2);
}
private Rotation randomRotation(RandomGenerator random) {
double q0 = random.nextDouble() * 2 - 1;
double q1 = random.nextDouble() * 2 - 1;
double q2 = random.nextDouble() * 2 - 1;
double q3 = random.nextDouble() * 2 - 1;
double q = FastMath.sqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
return new Rotation(q0 / q, q1 / q, q2 / q, q3 / q, false);
}
}