FieldPVCoordinates.java
/* Copyright 2002-2021 CS GROUP
* Licensed to CS GROUP (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
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package org.orekit.utils;
import org.hipparchus.Field;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.analysis.differentiation.FDSFactory;
import org.hipparchus.analysis.differentiation.FieldDerivative;
import org.hipparchus.analysis.differentiation.FieldDerivativeStructure;
import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative1;
import org.hipparchus.analysis.differentiation.FieldUnivariateDerivative2;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.util.FastMath;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitMessages;
import org.orekit.time.TimeShiftable;
/** Simple container for Position/Velocity pairs, using {@link CalculusFieldElement}.
* <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 FieldAngularCoordinates}.
* </p>
* <p>Instances of this class are guaranteed to be immutable.</p>
* @param <T> the type of the field elements
* @author Luc Maisonobe
* @since 6.0
* @see PVCoordinates
*/
public class FieldPVCoordinates<T extends CalculusFieldElement<T>>
implements TimeShiftable<FieldPVCoordinates<T>> {
/** The position. */
private final FieldVector3D<T> position;
/** The velocity. */
private final FieldVector3D<T> velocity;
/** The acceleration. */
private final FieldVector3D<T> acceleration;
/** Builds a FieldPVCoordinates triplet with zero acceleration.
* @param position the position vector (m)
* @param velocity the velocity vector (m/s)
*/
public FieldPVCoordinates(final FieldVector3D<T> position, final FieldVector3D<T> velocity) {
this.position = position;
this.velocity = velocity;
final T zero = position.getX().getField().getZero();
this.acceleration = new FieldVector3D<>(zero, zero, zero);
}
/** Builds a FieldPVCoordinates triplet.
* @param position the position vector (m)
* @param velocity the velocity vector (m/s)
* @param acceleration the acceleration vector (m/s²)
*/
public FieldPVCoordinates(final FieldVector3D<T> position, final FieldVector3D<T> velocity,
final FieldVector3D<T> acceleration) {
this.position = position;
this.velocity = velocity;
this.acceleration = acceleration;
}
/** Builds a FieldPVCoordinates from a field and a regular PVCoordinates.
* @param field field for the components
* @param pv PVCoordinates triplet to convert
*/
public FieldPVCoordinates(final Field<T> field, final PVCoordinates pv) {
this.position = new FieldVector3D<>(field, pv.getPosition());
this.velocity = new FieldVector3D<>(field, pv.getVelocity());
this.acceleration = new FieldVector3D<>(field, pv.getAcceleration());
}
/** 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 FieldPVCoordinates(final double a, final FieldPVCoordinates<T> pv) {
position = new FieldVector3D<>(a, pv.position);
velocity = new FieldVector3D<>(a, pv.velocity);
acceleration = new FieldVector3D<>(a, pv.acceleration);
}
/** 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 FieldPVCoordinates(final T a, final FieldPVCoordinates<T> pv) {
position = new FieldVector3D<>(a, pv.position);
velocity = new FieldVector3D<>(a, pv.velocity);
acceleration = new FieldVector3D<>(a, pv.acceleration);
}
/** 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 FieldPVCoordinates(final T a, final PVCoordinates pv) {
position = new FieldVector3D<>(a, pv.getPosition());
velocity = new FieldVector3D<>(a, pv.getVelocity());
acceleration = new FieldVector3D<>(a, pv.getAcceleration());
}
/** 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 FieldPVCoordinates(final FieldPVCoordinates<T> start, final FieldPVCoordinates<T> end) {
this.position = end.position.subtract(start.position);
this.velocity = end.velocity.subtract(start.velocity);
this.acceleration = end.acceleration.subtract(start.acceleration);
}
/** 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 FieldPVCoordinates(final double a1, final FieldPVCoordinates<T> pv1,
final double a2, final FieldPVCoordinates<T> pv2) {
position = new FieldVector3D<>(a1, pv1.position, a2, pv2.position);
velocity = new FieldVector3D<>(a1, pv1.velocity, a2, pv2.velocity);
acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration);
}
/** 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 FieldPVCoordinates(final T a1, final FieldPVCoordinates<T> pv1,
final T a2, final FieldPVCoordinates<T> pv2) {
position = new FieldVector3D<>(a1, pv1.position, a2, pv2.position);
velocity = new FieldVector3D<>(a1, pv1.velocity, a2, pv2.velocity);
acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration);
}
/** 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 FieldPVCoordinates(final T a1, final PVCoordinates pv1,
final T a2, final PVCoordinates pv2) {
position = new FieldVector3D<>(a1, pv1.getPosition(), a2, pv2.getPosition());
velocity = new FieldVector3D<>(a1, pv1.getVelocity(), a2, pv2.getVelocity());
acceleration = new FieldVector3D<>(a1, pv1.getAcceleration(), a2, pv2.getAcceleration());
}
/** 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 FieldPVCoordinates(final double a1, final FieldPVCoordinates<T> pv1,
final double a2, final FieldPVCoordinates<T> pv2,
final double a3, final FieldPVCoordinates<T> pv3) {
position = new FieldVector3D<>(a1, pv1.position, a2, pv2.position, a3, pv3.position);
velocity = new FieldVector3D<>(a1, pv1.velocity, a2, pv2.velocity, a3, pv3.velocity);
acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration, a3, pv3.acceleration);
}
/** 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 FieldPVCoordinates(final T a1, final FieldPVCoordinates<T> pv1,
final T a2, final FieldPVCoordinates<T> pv2,
final T a3, final FieldPVCoordinates<T> pv3) {
position = new FieldVector3D<>(a1, pv1.position, a2, pv2.position, a3, pv3.position);
velocity = new FieldVector3D<>(a1, pv1.velocity, a2, pv2.velocity, a3, pv3.velocity);
acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration, a3, pv3.acceleration);
}
/** 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 FieldPVCoordinates(final T a1, final PVCoordinates pv1,
final T a2, final PVCoordinates pv2,
final T a3, final PVCoordinates pv3) {
position = new FieldVector3D<>(a1, pv1.getPosition(), a2, pv2.getPosition(), a3, pv3.getPosition());
velocity = new FieldVector3D<>(a1, pv1.getVelocity(), a2, pv2.getVelocity(), a3, pv3.getVelocity());
acceleration = new FieldVector3D<>(a1, pv1.getAcceleration(), a2, pv2.getAcceleration(), a3, pv3.getAcceleration());
}
/** 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 FieldPVCoordinates(final double a1, final FieldPVCoordinates<T> pv1,
final double a2, final FieldPVCoordinates<T> pv2,
final double a3, final FieldPVCoordinates<T> pv3,
final double a4, final FieldPVCoordinates<T> pv4) {
position = new FieldVector3D<>(a1, pv1.position, a2, pv2.position, a3, pv3.position, a4, pv4.position);
velocity = new FieldVector3D<>(a1, pv1.velocity, a2, pv2.velocity, a3, pv3.velocity, a4, pv4.velocity);
acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration, a3, pv3.acceleration, a4, pv4.acceleration);
}
/** 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 FieldPVCoordinates(final T a1, final FieldPVCoordinates<T> pv1,
final T a2, final FieldPVCoordinates<T> pv2,
final T a3, final FieldPVCoordinates<T> pv3,
final T a4, final FieldPVCoordinates<T> pv4) {
position = new FieldVector3D<>(a1, pv1.position, a2, pv2.position, a3, pv3.position, a4, pv4.position);
velocity = new FieldVector3D<>(a1, pv1.velocity, a2, pv2.velocity, a3, pv3.velocity, a4, pv4.velocity);
acceleration = new FieldVector3D<>(a1, pv1.acceleration, a2, pv2.acceleration, a3, pv3.acceleration, a4, pv4.acceleration);
}
/** 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 FieldPVCoordinates(final T a1, final PVCoordinates pv1,
final T a2, final PVCoordinates pv2,
final T a3, final PVCoordinates pv3,
final T a4, final PVCoordinates pv4) {
position = new FieldVector3D<>(a1, pv1.getPosition(), a2, pv2.getPosition(),
a3, pv3.getPosition(), a4, pv4.getPosition());
velocity = new FieldVector3D<>(a1, pv1.getVelocity(), a2, pv2.getVelocity(),
a3, pv3.getVelocity(), a4, pv4.getVelocity());
acceleration = new FieldVector3D<>(a1, pv1.getAcceleration(), a2, pv2.getAcceleration(),
a3, pv3.getAcceleration(), a4, pv4.getAcceleration());
}
/** Builds a FieldPVCoordinates triplet from a {@link FieldVector3D}<{@link FieldDerivativeStructure}>.
* <p>
* The vector components must have time as their only derivation parameter and
* have consistent derivation orders.
* </p>
* @param p vector with time-derivatives embedded within the coordinates
* @param <U> type of the derivative
* @since 9.2
*/
public <U extends FieldDerivative<T, U>> FieldPVCoordinates(final FieldVector3D<U> p) {
position = new FieldVector3D<>(p.getX().getValue(), p.getY().getValue(), p.getZ().getValue());
if (p.getX().getOrder() >= 1) {
velocity = new FieldVector3D<>(p.getX().getPartialDerivative(1),
p.getY().getPartialDerivative(1),
p.getZ().getPartialDerivative(1));
if (p.getX().getOrder() >= 2) {
acceleration = new FieldVector3D<>(p.getX().getPartialDerivative(2),
p.getY().getPartialDerivative(2),
p.getZ().getPartialDerivative(2));
} else {
acceleration = FieldVector3D.getZero(position.getX().getField());
}
} else {
final FieldVector3D<T> zero = FieldVector3D.getZero(position.getX().getField());
velocity = zero;
acceleration = zero;
}
}
/** Get fixed position/velocity at origin (both p, v and a are zero vectors).
* @param field field for the components
* @param <T> the type of the field elements
* @return a new fixed position/velocity at origin
*/
public static <T extends CalculusFieldElement<T>> FieldPVCoordinates<T> getZero(final Field<T> field) {
return new FieldPVCoordinates<>(field, PVCoordinates.ZERO);
}
/** Transform the instance to a {@link FieldVector3D}<{@link FieldDerivativeStructure}>.
* <p>
* The {@link FieldDerivativeStructure} coordinates correspond to time-derivatives up
* to the user-specified order.
* </p>
* @param order derivation order for the vector components (must be either 0, 1 or 2)
* @return vector with time-derivatives embedded within the coordinates
* @since 9.2
*/
public FieldVector3D<FieldDerivativeStructure<T>> toDerivativeStructureVector(final int order) {
final FDSFactory<T> factory;
final FieldDerivativeStructure<T> x;
final FieldDerivativeStructure<T> y;
final FieldDerivativeStructure<T> z;
switch(order) {
case 0 :
factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
x = factory.build(position.getX());
y = factory.build(position.getY());
z = factory.build(position.getZ());
break;
case 1 :
factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
x = factory.build(position.getX(), velocity.getX());
y = factory.build(position.getY(), velocity.getY());
z = factory.build(position.getZ(), velocity.getZ());
break;
case 2 :
factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
x = factory.build(position.getX(), velocity.getX(), acceleration.getX());
y = factory.build(position.getY(), velocity.getY(), acceleration.getY());
z = factory.build(position.getZ(), velocity.getZ(), acceleration.getZ());
break;
default :
throw new OrekitException(OrekitMessages.OUT_OF_RANGE_DERIVATION_ORDER, order);
}
return new FieldVector3D<>(x, y, z);
}
/** Transform the instance to a {@link FieldVector3D}<{@link FieldUnivariateDerivative1}>.
* <p>
* The {@link FieldUnivariateDerivative1} coordinates correspond to time-derivatives up
* to the order 1.
* </p>
* @return vector with time-derivatives embedded within the coordinates
* @see #toUnivariateDerivative2Vector()
* @since 10.2
*/
public FieldVector3D<FieldUnivariateDerivative1<T>> toUnivariateDerivative1Vector() {
final FieldUnivariateDerivative1<T> x = new FieldUnivariateDerivative1<>(position.getX(), velocity.getX());
final FieldUnivariateDerivative1<T> y = new FieldUnivariateDerivative1<>(position.getY(), velocity.getY());
final FieldUnivariateDerivative1<T> z = new FieldUnivariateDerivative1<>(position.getZ(), velocity.getZ());
return new FieldVector3D<>(x, y, z);
}
/** Transform the instance to a {@link FieldVector3D}<{@link FieldUnivariateDerivative2}>.
* <p>
* The {@link FieldUnivariateDerivative2} coordinates correspond to time-derivatives up
* to the order 2.
* </p>
* @return vector with time-derivatives embedded within the coordinates
* @see #toUnivariateDerivative1Vector()
* @since 10.2
*/
public FieldVector3D<FieldUnivariateDerivative2<T>> toUnivariateDerivative2Vector() {
final FieldUnivariateDerivative2<T> x = new FieldUnivariateDerivative2<>(position.getX(), velocity.getX(), acceleration.getX());
final FieldUnivariateDerivative2<T> y = new FieldUnivariateDerivative2<>(position.getY(), velocity.getY(), acceleration.getY());
final FieldUnivariateDerivative2<T> z = new FieldUnivariateDerivative2<>(position.getZ(), velocity.getZ(), acceleration.getZ());
return new FieldVector3D<>(x, y, z);
}
/** Transform the instance to a {@link FieldPVCoordinates}<{@link FieldDerivativeStructure}>.
* <p>
* The {@link FieldDerivativeStructure} coordinates correspond to time-derivatives up
* to the user-specified order. As both the instance components {@link #getPosition() position},
* {@link #getVelocity() velocity} and {@link #getAcceleration() acceleration} and the
* {@link FieldDerivativeStructure#getPartialDerivative(int...) derivatives} of the components
* holds time-derivatives, there are several ways to retrieve these derivatives. If for example
* the {@code order} is set to 2, then both {@code pv.getPosition().getX().getPartialDerivative(2)},
* {@code pv.getVelocity().getX().getPartialDerivative(1)} and
* {@code pv.getAcceleration().getX().getValue()} return the exact same value.
* </p>
* <p>
* If derivation order is 1, the first derivative of acceleration will be computed as a
* Keplerian-only jerk. If derivation order is 2, the second derivative of velocity (which
* is also the first derivative of acceleration) will be computed as a Keplerian-only jerk,
* and the second derivative of acceleration will be computed as a Keplerian-only jounce.
* </p>
* @param order derivation order for the vector components (must be either 0, 1 or 2)
* @return pv coordinates with time-derivatives embedded within the coordinates
* @since 9.2
*/
public FieldPVCoordinates<FieldDerivativeStructure<T>> toDerivativeStructurePV(final int order) {
final FDSFactory<T> factory;
final FieldDerivativeStructure<T> x0;
final FieldDerivativeStructure<T> y0;
final FieldDerivativeStructure<T> z0;
final FieldDerivativeStructure<T> x1;
final FieldDerivativeStructure<T> y1;
final FieldDerivativeStructure<T> z1;
final FieldDerivativeStructure<T> x2;
final FieldDerivativeStructure<T> y2;
final FieldDerivativeStructure<T> z2;
switch(order) {
case 0 :
factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
x0 = factory.build(position.getX());
y0 = factory.build(position.getY());
z0 = factory.build(position.getZ());
x1 = factory.build(velocity.getX());
y1 = factory.build(velocity.getY());
z1 = factory.build(velocity.getZ());
x2 = factory.build(acceleration.getX());
y2 = factory.build(acceleration.getY());
z2 = factory.build(acceleration.getZ());
break;
case 1 : {
factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
final T r2 = position.getNormSq();
final T r = r2.sqrt();
final T pvOr2 = FieldVector3D.dotProduct(position, velocity).divide(r2);
final T a = acceleration.getNorm();
final T aOr = a.divide(r);
final FieldVector3D<T> keplerianJerk = new FieldVector3D<>(pvOr2.multiply(-3), acceleration,
aOr.negate(), velocity);
x0 = factory.build(position.getX(), velocity.getX());
y0 = factory.build(position.getY(), velocity.getY());
z0 = factory.build(position.getZ(), velocity.getZ());
x1 = factory.build(velocity.getX(), acceleration.getX());
y1 = factory.build(velocity.getY(), acceleration.getY());
z1 = factory.build(velocity.getZ(), acceleration.getZ());
x2 = factory.build(acceleration.getX(), keplerianJerk.getX());
y2 = factory.build(acceleration.getY(), keplerianJerk.getY());
z2 = factory.build(acceleration.getZ(), keplerianJerk.getZ());
break;
}
case 2 : {
factory = new FDSFactory<>(getPosition().getX().getField(), 1, order);
final T r2 = position.getNormSq();
final T r = r2.sqrt();
final T pvOr2 = FieldVector3D.dotProduct(position, velocity).divide(r2);
final T a = acceleration.getNorm();
final T aOr = a.divide(r);
final FieldVector3D<T> keplerianJerk = new FieldVector3D<>(pvOr2.multiply(-3), acceleration,
aOr.negate(), velocity);
final T v2 = velocity.getNormSq();
final T pa = FieldVector3D.dotProduct(position, acceleration);
final T aj = FieldVector3D.dotProduct(acceleration, keplerianJerk);
final FieldVector3D<T> keplerianJounce = new FieldVector3D<>(v2.add(pa).multiply(-3).divide(r2).add(pvOr2.multiply(pvOr2).multiply(15)).subtract(aOr), acceleration,
aOr.multiply(4).multiply(pvOr2).subtract(aj.divide(a.multiply(r))), velocity);
x0 = factory.build(position.getX(), velocity.getX(), acceleration.getX());
y0 = factory.build(position.getY(), velocity.getY(), acceleration.getY());
z0 = factory.build(position.getZ(), velocity.getZ(), acceleration.getZ());
x1 = factory.build(velocity.getX(), acceleration.getX(), keplerianJerk.getX());
y1 = factory.build(velocity.getY(), acceleration.getY(), keplerianJerk.getY());
z1 = factory.build(velocity.getZ(), acceleration.getZ(), keplerianJerk.getZ());
x2 = factory.build(acceleration.getX(), keplerianJerk.getX(), keplerianJounce.getX());
y2 = factory.build(acceleration.getY(), keplerianJerk.getY(), keplerianJounce.getY());
z2 = factory.build(acceleration.getZ(), keplerianJerk.getZ(), keplerianJounce.getZ());
break;
}
default :
throw new OrekitException(OrekitMessages.OUT_OF_RANGE_DERIVATION_ORDER, order);
}
return new FieldPVCoordinates<>(new FieldVector3D<>(x0, y0, z0),
new FieldVector3D<>(x1, y1, z1),
new FieldVector3D<>(x2, y2, z2));
}
/** Transform the instance to a {@link FieldPVCoordinates}<{@link FieldUnivariateDerivative1}>.
* <p>
* The {@link FieldUnivariateDerivative1} coordinates correspond to time-derivatives up
* to the order 1.
* The first derivative of acceleration will be computed as a Keplerian-only jerk.
* </p>
* @return pv coordinates with time-derivatives embedded within the coordinates
* @since 10.2
*/
public FieldPVCoordinates<FieldUnivariateDerivative1<T>> toUnivariateDerivative1PV() {
final T r2 = position.getNormSq();
final T r = FastMath.sqrt(r2);
final T pvOr2 = FieldVector3D.dotProduct(position, velocity).divide(r2);
final T a = acceleration.getNorm();
final T aOr = a.divide(r);
final FieldVector3D<T> keplerianJerk = new FieldVector3D<>(pvOr2.multiply(-3), acceleration,
aOr.negate(), velocity);
final FieldUnivariateDerivative1<T> x0 = new FieldUnivariateDerivative1<>(position.getX(), velocity.getX());
final FieldUnivariateDerivative1<T> y0 = new FieldUnivariateDerivative1<>(position.getY(), velocity.getY());
final FieldUnivariateDerivative1<T> z0 = new FieldUnivariateDerivative1<>(position.getZ(), velocity.getZ());
final FieldUnivariateDerivative1<T> x1 = new FieldUnivariateDerivative1<>(velocity.getX(), acceleration.getX());
final FieldUnivariateDerivative1<T> y1 = new FieldUnivariateDerivative1<>(velocity.getY(), acceleration.getY());
final FieldUnivariateDerivative1<T> z1 = new FieldUnivariateDerivative1<>(velocity.getZ(), acceleration.getZ());
final FieldUnivariateDerivative1<T> x2 = new FieldUnivariateDerivative1<>(acceleration.getX(), keplerianJerk.getX());
final FieldUnivariateDerivative1<T> y2 = new FieldUnivariateDerivative1<>(acceleration.getY(), keplerianJerk.getY());
final FieldUnivariateDerivative1<T> z2 = new FieldUnivariateDerivative1<>(acceleration.getZ(), keplerianJerk.getZ());
return new FieldPVCoordinates<>(new FieldVector3D<>(x0, y0, z0),
new FieldVector3D<>(x1, y1, z1),
new FieldVector3D<>(x2, y2, z2));
}
/** Transform the instance to a {@link FieldPVCoordinates}<{@link FieldUnivariateDerivative2}>.
* <p>
* The {@link FieldUnivariateDerivative2} coordinates correspond to time-derivatives up
* to the order 2.
* As derivation order is 2, the second derivative of velocity (which
* is also the first derivative of acceleration) will be computed as a Keplerian-only jerk,
* and the second derivative of acceleration will be computed as a Keplerian-only jounce.
* </p>
* @return pv coordinates with time-derivatives embedded within the coordinates
* @since 10.2
*/
public FieldPVCoordinates<FieldUnivariateDerivative2<T>> toUnivariateDerivative2PV() {
final T r2 = position.getNormSq();
final T r = r2.sqrt();
final T pvOr2 = FieldVector3D.dotProduct(position, velocity).divide(r2);
final T a = acceleration.getNorm();
final T aOr = a.divide(r);
final FieldVector3D<T> keplerianJerk = new FieldVector3D<>(pvOr2.multiply(-3), acceleration,
aOr.negate(), velocity);
final T v2 = velocity.getNormSq();
final T pa = FieldVector3D.dotProduct(position, acceleration);
final T aj = FieldVector3D.dotProduct(acceleration, keplerianJerk);
final FieldVector3D<T> keplerianJounce = new FieldVector3D<>(v2.add(pa).multiply(-3).divide(r2).add(pvOr2.multiply(pvOr2).multiply(15)).subtract(aOr), acceleration,
aOr.multiply(4).multiply(pvOr2).subtract(aj.divide(a.multiply(r))), velocity);
final FieldUnivariateDerivative2<T> x0 = new FieldUnivariateDerivative2<>(position.getX(), velocity.getX(), acceleration.getX());
final FieldUnivariateDerivative2<T> y0 = new FieldUnivariateDerivative2<>(position.getY(), velocity.getY(), acceleration.getY());
final FieldUnivariateDerivative2<T> z0 = new FieldUnivariateDerivative2<>(position.getZ(), velocity.getZ(), acceleration.getZ());
final FieldUnivariateDerivative2<T> x1 = new FieldUnivariateDerivative2<>(velocity.getX(), acceleration.getX(), keplerianJerk.getX());
final FieldUnivariateDerivative2<T> y1 = new FieldUnivariateDerivative2<>(velocity.getY(), acceleration.getY(), keplerianJerk.getY());
final FieldUnivariateDerivative2<T> z1 = new FieldUnivariateDerivative2<>(velocity.getZ(), acceleration.getZ(), keplerianJerk.getZ());
final FieldUnivariateDerivative2<T> x2 = new FieldUnivariateDerivative2<>(acceleration.getX(), keplerianJerk.getX(), keplerianJounce.getX());
final FieldUnivariateDerivative2<T> y2 = new FieldUnivariateDerivative2<>(acceleration.getY(), keplerianJerk.getY(), keplerianJounce.getY());
final FieldUnivariateDerivative2<T> z2 = new FieldUnivariateDerivative2<>(acceleration.getZ(), keplerianJerk.getZ(), keplerianJounce.getZ());
return new FieldPVCoordinates<>(new FieldVector3D<>(x0, y0, z0),
new FieldVector3D<>(x1, y1, z1),
new FieldVector3D<>(x2, y2, z2));
}
/** 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
* @param <T> the type of the field elements
* @return velocity allowing to go from start to end positions
*/
public static <T extends CalculusFieldElement<T>> FieldVector3D<T> estimateVelocity(final FieldVector3D<T> start,
final FieldVector3D<T> end,
final double dt) {
final double scale = 1.0 / dt;
return new FieldVector3D<>(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 quadratic 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 FieldPVCoordinates<T> shiftedBy(final double dt) {
return new FieldPVCoordinates<>(new FieldVector3D<>(1, position, dt, velocity, 0.5 * dt * dt, acceleration),
new FieldVector3D<>(1, velocity, dt, acceleration),
acceleration);
}
/** Get a time-shifted state.
* <p>
* The state can be slightly shifted to close dates. This shift is based on
* a simple quadratic 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 FieldPVCoordinates<T> shiftedBy(final T dt) {
final T one = dt.getField().getOne();
return new FieldPVCoordinates<>(new FieldVector3D<>(one, position,
dt, velocity,
dt.multiply(dt).multiply(0.5), acceleration),
new FieldVector3D<>(one, velocity,
dt, acceleration),
acceleration);
}
/** Gets the position.
* @return the position vector (m).
*/
public FieldVector3D<T> getPosition() {
return position;
}
/** Gets the velocity.
* @return the velocity vector (m/s).
*/
public FieldVector3D<T> getVelocity() {
return velocity;
}
/** Gets the acceleration.
* @return the acceleration vector (m/s²).
*/
public FieldVector3D<T> getAcceleration() {
return acceleration;
}
/** 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 (m²/s).
*/
public FieldVector3D<T> getMomentum() {
return FieldVector3D.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||²
*
* @return the angular velocity vector
* @see <a href="http://en.wikipedia.org/wiki/Angular_velocity">Angular Velocity on
* Wikipedia</a>
*/
public FieldVector3D<T> getAngularVelocity() {
return this.getMomentum().scalarMultiply(
this.getPosition().getNormSq().reciprocal());
}
/** Get the opposite of the instance.
* @return a new position-velocity which is opposite to the instance
*/
public FieldPVCoordinates<T> negate() {
return new FieldPVCoordinates<>(position.negate(), velocity.negate(), acceleration.negate());
}
/** Normalize the position part of the instance.
* <p>
* The computed coordinates first component (position) will be a
* normalized vector, the second component (velocity) will be the
* derivative of the first component (hence it will generally not
* be normalized), and the third component (acceleration) will be the
* derivative of the second component (hence it will generally not
* be normalized).
* </p>
* @return a new instance, with first component normalized and
* remaining component computed to have consistent derivatives
*/
public FieldPVCoordinates<T> normalize() {
final T inv = position.getNorm().reciprocal();
final FieldVector3D<T> u = new FieldVector3D<>(inv, position);
final FieldVector3D<T> v = new FieldVector3D<>(inv, velocity);
final FieldVector3D<T> w = new FieldVector3D<>(inv, acceleration);
final T uv = FieldVector3D.dotProduct(u, v);
final T v2 = FieldVector3D.dotProduct(v, v);
final T uw = FieldVector3D.dotProduct(u, w);
final FieldVector3D<T> uDot = new FieldVector3D<>(inv.getField().getOne(), v,
uv.multiply(-1), u);
final FieldVector3D<T> uDotDot = new FieldVector3D<>(inv.getField().getOne(), w,
uv.multiply(-2), v,
uv.multiply(uv).multiply(3).subtract(v2).subtract(uw), u);
return new FieldPVCoordinates<>(u, uDot, uDotDot);
}
/** Compute the cross-product of two instances.
* @param pv2 second instances
* @return the cross product v1 ^ v2 as a new instance
*/
public FieldPVCoordinates<T> crossProduct(final FieldPVCoordinates<T> pv2) {
final FieldVector3D<T> p1 = position;
final FieldVector3D<T> v1 = velocity;
final FieldVector3D<T> a1 = acceleration;
final FieldVector3D<T> p2 = pv2.position;
final FieldVector3D<T> v2 = pv2.velocity;
final FieldVector3D<T> a2 = pv2.acceleration;
return new FieldPVCoordinates<>(FieldVector3D.crossProduct(p1, p2),
new FieldVector3D<>(1, FieldVector3D.crossProduct(p1, v2),
1, FieldVector3D.crossProduct(v1, p2)),
new FieldVector3D<>(1, FieldVector3D.crossProduct(p1, a2),
2, FieldVector3D.crossProduct(v1, v2),
1, FieldVector3D.crossProduct(a1, p2)));
}
/** Convert to a constant position-velocity.
* @return a constant position-velocity
*/
public PVCoordinates toPVCoordinates() {
return new PVCoordinates(position.toVector3D(), velocity.toVector3D(), acceleration.toVector3D());
}
/** 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().getReal()).append(comma).
append(position.getY().getReal()).append(comma).
append(position.getZ().getReal()).append("), V(").
append(velocity.getX().getReal()).append(comma).
append(velocity.getY().getReal()).append(comma).
append(velocity.getZ().getReal()).append("), A(").
append(acceleration.getX().getReal()).append(comma).
append(acceleration.getY().getReal()).append(comma).
append(acceleration.getZ().getReal()).append(")}").toString();
}
}