PVCoordinates.java
/* Copyright 2002-2013 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.io.Serializable;
import java.util.Collection;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.analysis.interpolation.HermiteInterpolator;
import org.apache.commons.math3.geometry.euclidean.threed.Vector3D;
import org.apache.commons.math3.util.Pair;
import org.orekit.time.AbsoluteDate;
import org.orekit.time.TimeShiftable;
/** Simple container for Position/Velocity pairs.
* <p>
* The state can be slightly shifted to close dates. This shift is based on
* a simple linear model. It is <em>not</em> intended as a replacement for
* proper orbit propagation (it is not even Keplerian!) but should be sufficient
* for either small time shifts or coarse accuracy.
* </p>
* <p>
* This class is the angular counterpart to {@link AngularCoordinates}.
* </p>
* <p>Instances of this class are guaranteed to be immutable.</p>
* @author Fabien Maussion
* @author Luc Maisonobe
*/
public class PVCoordinates implements TimeShiftable<PVCoordinates>, Serializable {
/** Fixed position/velocity at origin (both p and v are zero vectors). */
public static final PVCoordinates ZERO = new PVCoordinates(Vector3D.ZERO, Vector3D.ZERO);
/** Serializable UID. */
private static final long serialVersionUID = 4157449919684833834L;
/** The position. */
private final Vector3D position;
/** The velocity. */
private final Vector3D velocity;
/** Simple constructor.
* <p> Sets the Coordinates to default : (0 0 0) (0 0 0).</p>
*/
public PVCoordinates() {
position = Vector3D.ZERO;
velocity = Vector3D.ZERO;
}
/** Builds a PVCoordinates pair.
* @param position the position vector (m)
* @param velocity the velocity vector (m/s)
*/
public PVCoordinates(final Vector3D position, final Vector3D velocity) {
this.position = position;
this.velocity = velocity;
}
/** Multiplicative constructor
* <p>Build a PVCoordinates from another one and a scale factor.</p>
* <p>The PVCoordinates built will be a * pv</p>
* @param a scale factor
* @param pv base (unscaled) PVCoordinates
*/
public PVCoordinates(final double a, final PVCoordinates pv) {
position = new Vector3D(a, pv.position);
velocity = new Vector3D(a, pv.velocity);
}
/** Subtractive constructor
* <p>Build a relative PVCoordinates from a start and an end position.</p>
* <p>The PVCoordinates built will be end - start.</p>
* @param start Starting PVCoordinates
* @param end ending PVCoordinates
*/
public PVCoordinates(final PVCoordinates start, final PVCoordinates end) {
this.position = end.position.subtract(start.position);
this.velocity = end.velocity.subtract(start.velocity);
}
/** Linear constructor
* <p>Build a PVCoordinates from two other ones and corresponding scale factors.</p>
* <p>The PVCoordinates built will be a1 * u1 + a2 * u2</p>
* @param a1 first scale factor
* @param pv1 first base (unscaled) PVCoordinates
* @param a2 second scale factor
* @param pv2 second base (unscaled) PVCoordinates
*/
public PVCoordinates(final double a1, final PVCoordinates pv1,
final double a2, final PVCoordinates pv2) {
position = new Vector3D(a1, pv1.position, a2, pv2.position);
velocity = new Vector3D(a1, pv1.velocity, a2, pv2.velocity);
}
/** Linear constructor
* <p>Build a PVCoordinates from three other ones and corresponding scale factors.</p>
* <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3</p>
* @param a1 first scale factor
* @param pv1 first base (unscaled) PVCoordinates
* @param a2 second scale factor
* @param pv2 second base (unscaled) PVCoordinates
* @param a3 third scale factor
* @param pv3 third base (unscaled) PVCoordinates
*/
public PVCoordinates(final double a1, final PVCoordinates pv1,
final double a2, final PVCoordinates pv2,
final double a3, final PVCoordinates pv3) {
position = new Vector3D(a1, pv1.position, a2, pv2.position, a3, pv3.position);
velocity = new Vector3D(a1, pv1.velocity, a2, pv2.velocity, a3, pv3.velocity);
}
/** Linear constructor
* <p>Build a PVCoordinates from four other ones and corresponding scale factors.</p>
* <p>The PVCoordinates built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4</p>
* @param a1 first scale factor
* @param pv1 first base (unscaled) PVCoordinates
* @param a2 second scale factor
* @param pv2 second base (unscaled) PVCoordinates
* @param a3 third scale factor
* @param pv3 third base (unscaled) PVCoordinates
* @param a4 fourth scale factor
* @param pv4 fourth base (unscaled) PVCoordinates
*/
public PVCoordinates(final double a1, final PVCoordinates pv1,
final double a2, final PVCoordinates pv2,
final double a3, final PVCoordinates pv3,
final double a4, final PVCoordinates pv4) {
position = new Vector3D(a1, pv1.position, a2, pv2.position, a3, pv3.position, a4, pv4.position);
velocity = new Vector3D(a1, pv1.velocity, a2, pv2.velocity, a3, pv3.velocity, a4, pv4.velocity);
}
/** Estimate velocity between two positions.
* <p>Estimation is based on a simple fixed velocity translation
* during the time interval between the two positions.</p>
* @param start start position
* @param end end position
* @param dt time elapsed between the dates of the two positions
* @return velocity allowing to go from start to end positions
*/
public static Vector3D estimateVelocity(final Vector3D start, final Vector3D end, final double dt) {
final double scale = 1.0 / dt;
return new Vector3D(scale, end, -scale, start);
}
/** Get a time-shifted state.
* <p>
* The state can be slightly shifted to close dates. This shift is based on
* a simple linear model. It is <em>not</em> intended as a replacement for
* proper orbit propagation (it is not even Keplerian!) but should be sufficient
* for either small time shifts or coarse accuracy.
* </p>
* @param dt time shift in seconds
* @return a new state, shifted with respect to the instance (which is immutable)
*/
public PVCoordinates shiftedBy(final double dt) {
return new PVCoordinates(new Vector3D(1, position, dt, velocity), velocity);
}
/** Interpolate position-velocity.
* <p>
* The interpolated instance is created by polynomial Hermite interpolation
* ensuring velocity remains the exact derivative of position.
* </p>
* <p>
* Note that even if first time derivatives (velocities)
* from sample can be ignored, the interpolated instance always includes
* interpolated derivatives. This feature can be used explicitly to
* compute these derivatives when it would be too complex to compute them
* from an analytical formula: just compute a few sample points from the
* explicit formula and set the derivatives to zero in these sample points,
* then use interpolation to add derivatives consistent with the positions.
* </p>
* @param date interpolation date
* @param useVelocities if true, use sample points velocities,
* otherwise ignore them and use only positions
* @param sample sample points on which interpolation should be done
* @return a new position-velocity, interpolated at specified date
*/
public static PVCoordinates interpolate(final AbsoluteDate date, final boolean useVelocities,
final Collection<Pair<AbsoluteDate, PVCoordinates>> sample) {
// set up an interpolator taking derivatives into account
final HermiteInterpolator interpolator = new HermiteInterpolator();
// add sample points
if (useVelocities) {
// populate sample with position and velocity data
for (final Pair<AbsoluteDate, PVCoordinates> datedPV : sample) {
final Vector3D position = datedPV.getValue().getPosition();
final Vector3D velocity = datedPV.getValue().getVelocity();
interpolator.addSamplePoint(datedPV.getKey().getDate().durationFrom(date),
new double[] {
position.getX(), position.getY(), position.getZ()
}, new double[] {
velocity.getX(), velocity.getY(), velocity.getZ()
});
}
} else {
// populate sample with position data, ignoring velocity
for (final Pair<AbsoluteDate, PVCoordinates> datedPV : sample) {
final Vector3D position = datedPV.getValue().getPosition();
interpolator.addSamplePoint(datedPV.getKey().getDate().durationFrom(date),
new double[] {
position.getX(), position.getY(), position.getZ()
});
}
}
// interpolate
final DerivativeStructure zero = new DerivativeStructure(1, 1, 0, 0.0);
final DerivativeStructure[] p = interpolator.value(zero);
// build a new interpolated instance
return new PVCoordinates(new Vector3D(p[0].getValue(),
p[1].getValue(),
p[2].getValue()),
new Vector3D(p[0].getPartialDerivative(1),
p[1].getPartialDerivative(1),
p[2].getPartialDerivative(1)));
}
/** Gets the position.
* @return the position vector (m).
*/
public Vector3D getPosition() {
return position;
}
/** Gets the velocity.
* @return the velocity vector (m/s).
*/
public Vector3D getVelocity() {
return velocity;
}
/** Gets the momentum.
* <p>This vector is the p ⊗ v where p is position, v is velocity
* and ⊗ is cross product. To get the real physical angular momentum
* you need to multiply this vector by the mass.</p>
* <p>The returned vector is recomputed each time this method is called, it
* is not cached.</p>
* @return a new instance of the momentum vector (m<sup>2</sup>/s).
*/
public Vector3D getMomentum() {
return Vector3D.crossProduct(position, velocity);
}
/**
* Get the angular velocity (spin) of this point as seen from the origin.
* <p/>
* The angular velocity vector is parallel to the {@link #getMomentum() angular
* momentum} and is computed by ω = p × v / ||p||<sup>2</sup>
*
* @return the angular velocity vector
* @see <a href="http://en.wikipedia.org/wiki/Angular_velocity">Angular Velocity on
* Wikipedia</a>
*/
public Vector3D getAngularVelocity() {
return this.getMomentum().scalarMultiply(1.0 / this.getPosition().getNormSq());
}
/** Get the opposite of the instance.
* @return a new position-velocity which is opposite to the instance
*/
public PVCoordinates negate() {
return new PVCoordinates(position.negate(), velocity.negate());
}
/** Return a string representation of this position/velocity pair.
* @return string representation of this position/velocity pair
*/
public String toString() {
final String comma = ", ";
return new StringBuffer().append('{').append("P(").
append(position.getX()).append(comma).
append(position.getY()).append(comma).
append(position.getZ()).append("), V(").
append(velocity.getX()).append(comma).
append(velocity.getY()).append(comma).
append(velocity.getZ()).append(")}").toString();
}
}