SmallManeuverAnalyticalModel.java
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package org.orekit.forces.maneuvers;
import java.util.Arrays;
import org.hipparchus.geometry.euclidean.threed.Vector3D;
import org.hipparchus.util.FastMath;
import org.orekit.frames.Frame;
import org.orekit.orbits.Orbit;
import org.orekit.orbits.OrbitType;
import org.orekit.orbits.PositionAngleType;
import org.orekit.propagation.SpacecraftState;
import org.orekit.propagation.analytical.AdapterPropagator;
import org.orekit.time.AbsoluteDate;
import org.orekit.utils.Constants;
/** Analytical model for small maneuvers.
* <p>The aim of this model is to compute quickly the effect at date t₁
* of a small maneuver performed at an earlier date t₀. Both the
* direct effect of the maneuver and the Jacobian of this effect with respect to
* maneuver parameters are available.
* </p>
* <p>These effect are computed analytically using two Jacobian matrices:
* <ol>
* <li>J₀: Jacobian of Keplerian or equinoctial elements with respect
* to Cartesian parameters at date t₀ allows to compute
* maneuver effect as a change in orbital elements at maneuver date t₀,</li>
* <li>J<sub>1/0</sub>: Jacobian of Keplerian or equinoctial elements
* at date t₁ with respect to Keplerian or equinoctial elements
* at date t₀ allows to propagate the change in orbital elements
* to final date t₁.</li>
* </ol>
*
* <p>
* The second Jacobian, J<sub>1/0</sub>, is computed using a simple Keplerian
* model, i.e. it is the identity except for the mean motion row which also includes
* an off-diagonal element due to semi-major axis change.
* </p>
* <p>
* The orbital elements change at date t₁ can be added to orbital elements
* extracted from state, and the final elements taking account the changes are then
* converted back to appropriate type, which may be different from Keplerian or
* equinoctial elements.
* </p>
* <p>
* Note that this model takes <em>only</em> Keplerian effects into account. This means
* that using only this class to compute an inclination maneuver in Low Earth Orbit will
* <em>not</em> change ascending node drift rate despite inclination has changed (the
* same would be true for a semi-major axis change of course). In order to take this
* drift into account, an instance of {@link
* org.orekit.propagation.analytical.J2DifferentialEffect J2DifferentialEffect}
* must be used together with an instance of this class.
* </p>
* @author Luc Maisonobe
*/
public class SmallManeuverAnalyticalModel
implements AdapterPropagator.DifferentialEffect {
/** State at maneuver date (before maneuver occurrence). */
private final SpacecraftState state0;
/** Inertial velocity increment. */
private final Vector3D inertialDV;
/** Mass change ratio. */
private final double massRatio;
/** Type of orbit used for internal Jacobians. */
private final OrbitType type;
/** Initial Keplerian (or equinoctial) Jacobian with respect to maneuver. */
private final double[][] j0;
/** Time derivative of the initial Keplerian (or equinoctial) Jacobian with respect to maneuver. */
private double[][] j0Dot;
/** Mean anomaly change factor. */
private final double ksi;
/** Build a maneuver defined in spacecraft frame.
* @param state0 state at maneuver date, <em>before</em> the maneuver
* is performed
* @param dV velocity increment in spacecraft frame
* @param isp engine specific impulse (s)
*/
public SmallManeuverAnalyticalModel(final SpacecraftState state0,
final Vector3D dV, final double isp) {
this(state0, state0.getFrame(),
state0.getAttitude().getRotation().applyInverseTo(dV),
isp);
}
/** Build a maneuver defined in user-specified frame.
* @param state0 state at maneuver date, <em>before</em> the maneuver
* is performed
* @param frame frame in which velocity increment is defined
* @param dV velocity increment in specified frame
* @param isp engine specific impulse (s)
*/
public SmallManeuverAnalyticalModel(final SpacecraftState state0, final Frame frame,
final Vector3D dV, final double isp) {
this.state0 = state0;
this.massRatio = FastMath.exp(-dV.getNorm() / (Constants.G0_STANDARD_GRAVITY * isp));
// use equinoctial orbit type if possible, Keplerian if nearly hyperbolic orbits
type = (state0.getE() < 0.9) ? OrbitType.EQUINOCTIAL : OrbitType.KEPLERIAN;
// compute initial Jacobian
final double[][] fullJacobian = new double[6][6];
j0 = new double[6][3];
final Orbit orbit0 = type.convertType(state0.getOrbit());
orbit0.getJacobianWrtCartesian(PositionAngleType.MEAN, fullJacobian);
for (int i = 0; i < j0.length; ++i) {
System.arraycopy(fullJacobian[i], 3, j0[i], 0, 3);
}
// use lazy evaluation for j0Dot, as it is used only when Jacobians are evaluated
j0Dot = null;
// compute maneuver effect on Keplerian (or equinoctial) elements
inertialDV = frame.getStaticTransformTo(state0.getFrame(), state0.getDate())
.transformVector(dV);
// compute mean anomaly change: dM(t1) = dM(t0) + ksi * da * (t1 - t0)
final double mu = state0.getMu();
final double a = state0.getA();
ksi = -1.5 * FastMath.sqrt(mu / a) / (a * a);
}
/** Get the date of the maneuver.
* @return date of the maneuver
*/
public AbsoluteDate getDate() {
return state0.getDate();
}
/** Get the inertial velocity increment of the maneuver.
* @return velocity increment in a state-dependent inertial frame
* @see #getInertialFrame()
*/
public Vector3D getInertialDV() {
return inertialDV;
}
/** Get the inertial frame in which the velocity increment is defined.
* @return inertial frame in which the velocity increment is defined
* @see #getInertialDV()
*/
public Frame getInertialFrame() {
return state0.getFrame();
}
/** Compute the effect of the maneuver on an orbit.
* @param orbit1 original orbit at t₁, without maneuver
* @return orbit at t₁, taking the maneuver
* into account if t₁ > t₀
* @see #apply(SpacecraftState)
* @see #getJacobian(Orbit, PositionAngleType, double[][])
*/
public Orbit apply(final Orbit orbit1) {
if (orbit1.getDate().compareTo(state0.getDate()) <= 0) {
// the maneuver has not occurred yet, don't change anything
return orbit1;
}
return orbit1.getType().convertType(updateOrbit(orbit1));
}
/** Compute the effect of the maneuver on a spacecraft state.
* @param state1 original spacecraft state at t₁,
* without maneuver
* @return spacecraft state at t₁, taking the maneuver
* into account if t₁ > t₀
* @see #apply(Orbit)
* @see #getJacobian(Orbit, PositionAngleType, double[][])
*/
public SpacecraftState apply(final SpacecraftState state1) {
if (state1.getDate().compareTo(state0.getDate()) <= 0) {
// the maneuver has not occurred yet, don't change anything
return state1;
}
return new SpacecraftState(state1.getOrbit().getType().convertType(updateOrbit(state1.getOrbit())),
state1.getAttitude(), updateMass(state1.getMass()));
}
/** Compute the effect of the maneuver on an orbit.
* @param orbit1 original orbit at t₁, without maneuver
* @return orbit at t₁, always taking the maneuver into account, always in the internal type
*/
private Orbit updateOrbit(final Orbit orbit1) {
// compute maneuver effect
final double dt = orbit1.getDate().durationFrom(state0.getDate());
final double x = inertialDV.getX();
final double y = inertialDV.getY();
final double z = inertialDV.getZ();
final double[] delta = new double[6];
for (int i = 0; i < delta.length; ++i) {
delta[i] = j0[i][0] * x + j0[i][1] * y + j0[i][2] * z;
}
delta[5] += ksi * delta[0] * dt;
// convert current orbital state to Keplerian or equinoctial elements
final double[] parameters = new double[6];
type.mapOrbitToArray(type.convertType(orbit1), PositionAngleType.MEAN, parameters, null);
for (int i = 0; i < delta.length; ++i) {
parameters[i] += delta[i];
}
// build updated orbit as Keplerian or equinoctial elements
return type.mapArrayToOrbit(parameters, null, PositionAngleType.MEAN,
orbit1.getDate(), orbit1.getMu(), orbit1.getFrame());
}
/** Compute the Jacobian of the orbit with respect to maneuver parameters.
* <p>
* The Jacobian matrix is a 6x4 matrix. Element jacobian[i][j] corresponds to
* the partial derivative of orbital parameter i with respect to maneuver
* parameter j. The rows order is the same order as used in {@link
* Orbit#getJacobianWrtCartesian(PositionAngleType, double[][]) Orbit.getJacobianWrtCartesian}
* method. Columns (0, 1, 2) correspond to the velocity increment coordinates
* (ΔV<sub>x</sub>, ΔV<sub>y</sub>, ΔV<sub>z</sub>) in the
* inertial frame returned by {@link #getInertialFrame()}, and column 3
* corresponds to the maneuver date t₀.
* </p>
* @param orbit1 original orbit at t₁, without maneuver
* @param positionAngleType type of the position angle to use
* @param jacobian placeholder 6x4 (or larger) matrix to be filled with the Jacobian, if matrix
* is larger than 6x4, only the 6x4 upper left corner will be modified
* @see #apply(Orbit)
*/
public void getJacobian(final Orbit orbit1, final PositionAngleType positionAngleType,
final double[][] jacobian) {
final double dt = orbit1.getDate().durationFrom(state0.getDate());
if (dt < 0) {
// the maneuver has not occurred yet, Jacobian is null
for (int i = 0; i < 6; ++i) {
Arrays.fill(jacobian[i], 0, 4, 0.0);
}
return;
}
// derivatives of Keplerian/equinoctial elements with respect to velocity increment
final double x = inertialDV.getX();
final double y = inertialDV.getY();
final double z = inertialDV.getZ();
for (int i = 0; i < 6; ++i) {
System.arraycopy(j0[i], 0, jacobian[i], 0, 3);
}
for (int j = 0; j < 3; ++j) {
jacobian[5][j] += ksi * dt * j0[0][j];
}
// derivatives of Keplerian/equinoctial elements with respect to date
evaluateJ0Dot();
for (int i = 0; i < 6; ++i) {
jacobian[i][3] = j0Dot[i][0] * x + j0Dot[i][1] * y + j0Dot[i][2] * z;
}
final double da = j0[0][0] * x + j0[0][1] * y + j0[0][2] * z;
jacobian[5][3] += ksi * (jacobian[0][3] * dt - da);
if (orbit1.getType() != type || positionAngleType != PositionAngleType.MEAN) {
// convert to derivatives of Cartesian parameters
final double[][] j2 = new double[6][6];
final double[][] pvJacobian = new double[6][4];
final Orbit updated = updateOrbit(orbit1);
updated.getJacobianWrtParameters(PositionAngleType.MEAN, j2);
for (int i = 0; i < 6; ++i) {
for (int j = 0; j < 4; ++j) {
pvJacobian[i][j] = j2[i][0] * jacobian[0][j] + j2[i][1] * jacobian[1][j] +
j2[i][2] * jacobian[2][j] + j2[i][3] * jacobian[3][j] +
j2[i][4] * jacobian[4][j] + j2[i][5] * jacobian[5][j];
}
}
// convert to derivatives of specified parameters
final double[][] j3 = new double[6][6];
orbit1.getType().convertType(updated).getJacobianWrtCartesian(positionAngleType, j3);
for (int j = 0; j < 4; ++j) {
for (int i = 0; i < 6; ++i) {
jacobian[i][j] = j3[i][0] * pvJacobian[0][j] + j3[i][1] * pvJacobian[1][j] +
j3[i][2] * pvJacobian[2][j] + j3[i][3] * pvJacobian[3][j] +
j3[i][4] * pvJacobian[4][j] + j3[i][5] * pvJacobian[5][j];
}
}
}
}
/** Lazy evaluation of the initial Jacobian time derivative.
*/
private void evaluateJ0Dot() {
if (j0Dot == null) {
j0Dot = new double[6][3];
final double dt = 1.0e-5 / state0.getOrbit().getKeplerianMeanMotion();
final Orbit orbit = type.convertType(state0.getOrbit());
// compute shifted Jacobians
final double[][] j0m1 = new double[6][6];
orbit.shiftedBy(-1 * dt).getJacobianWrtCartesian(PositionAngleType.MEAN, j0m1);
final double[][] j0p1 = new double[6][6];
orbit.shiftedBy(+1 * dt).getJacobianWrtCartesian(PositionAngleType.MEAN, j0p1);
// evaluate derivative by finite differences
for (int i = 0; i < j0Dot.length; ++i) {
final double[] m1Row = j0m1[i];
final double[] p1Row = j0p1[i];
final double[] j0DotRow = j0Dot[i];
for (int j = 0; j < 3; ++j) {
j0DotRow[j] = (p1Row[j + 3] - m1Row[j + 3]) / (2 * dt);
}
}
}
}
/** Update a spacecraft mass due to maneuver.
* @param mass masse before maneuver
* @return mass after maneuver
*/
public double updateMass(final double mass) {
return massRatio * mass;
}
}