org.orekit.utils

Class AngularCoordinates

java.lang.Object

org.orekit.utils.AngularCoordinates

All Implemented Interfaces:

Serializable, TimeShiftable<AngularCoordinates>

Direct Known Subclasses:

TimeStampedAngularCoordinates

public class AngularCoordinates
extends Object
implements TimeShiftable<AngularCoordinates>, Serializable

Simple container for rotation/rotation rate/rotation acceleration triplets.

The state can be slightly shifted to close dates. This shift is based on an approximate solution of the fixed acceleration motion. It is not intended as a replacement for proper attitude propagation but should be sufficient for either small time shifts or coarse accuracy.

This class is the angular counterpart to PVCoordinates.

Instances of this class are guaranteed to be immutable.

Author:

Luc Maisonobe

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static AngularCoordinates	IDENTITY Fixed orientation parallel with reference frame (identity rotation, zero rotation rate and acceleration).

Constructor Summary

Constructors

Constructor and Description
AngularCoordinates() Simple constructor.
AngularCoordinates(FieldRotation<DerivativeStructure> r) Builds a AngularCoordinates from a FieldRotation<DerivativeStructure>.
AngularCoordinates(PVCoordinates u, PVCoordinates v) Build one of the rotations that transform one pv coordinates into another one.
AngularCoordinates(PVCoordinates u1, PVCoordinates u2, PVCoordinates v1, PVCoordinates v2, double tolerance) Build the rotation that transforms a pair of pv coordinates into another one.
AngularCoordinates(Rotation rotation, Vector3D rotationRate) Builds a rotation/rotation rate pair.
AngularCoordinates(Rotation rotation, Vector3D rotationRate, Vector3D rotationAcceleration) Builds a rotation/rotation rate/rotation acceleration triplet.

Method Summary

Methods

Modifier and Type	Method and Description
AngularCoordinates	addOffset(AngularCoordinates offset) Add an offset from the instance.
PVCoordinates	applyTo(PVCoordinates pv) Apply the rotation to a pv coordinates.
TimeStampedPVCoordinates	applyTo(TimeStampedPVCoordinates pv) Apply the rotation to a pv coordinates.
static AngularCoordinates	createFromModifiedRodrigues(double[][] r) Convert a modified Rodrigues vector and derivatives to angular coordinates.
static Vector3D	estimateRate(Rotation start, Rotation end, double dt) Estimate rotation rate between two orientations.
double[][]	getModifiedRodrigues(double sign) Convert rotation, rate and acceleration to modified Rodrigues vector and derivatives.
Rotation	getRotation() Get the rotation.
Vector3D	getRotationAcceleration() Get the rotation acceleration.
Vector3D	getRotationRate() Get the rotation rate.
static AngularCoordinates	interpolate(AbsoluteDate date, boolean useRotationRates, Collection<Pair<AbsoluteDate,AngularCoordinates>> sample) Deprecated. since 7.0 replaced with TimeStampedAngularCoordinates.interpolate(AbsoluteDate, AngularDerivativesFilter, Collection)
AngularCoordinates	revert() Revert a rotation/rotation rate/ rotation acceleration triplet.
AngularCoordinates	shiftedBy(double dt) Get a time-shifted state.
AngularCoordinates	subtractOffset(AngularCoordinates offset) Subtract an offset from the instance.
FieldRotation<DerivativeStructure>	toDerivativeStructureRotation(int order) Transform the instance to a FieldRotation<DerivativeStructure>.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

IDENTITY

public static final AngularCoordinates IDENTITY

Fixed orientation parallel with reference frame (identity rotation, zero rotation rate and acceleration).

Constructor Detail

AngularCoordinates

public AngularCoordinates()

Simple constructor.

Sets the Coordinates to default : Identity, Ω = (0 0 0), dΩ/dt = (0 0 0).

AngularCoordinates

public AngularCoordinates(Rotation rotation,
                  Vector3D rotationRate)

Builds a rotation/rotation rate pair.

Parameters:

rotation - rotation

rotationRate - rotation rate Ω (rad/s)

AngularCoordinates

public AngularCoordinates(Rotation rotation,
                  Vector3D rotationRate,
                  Vector3D rotationAcceleration)

Builds a rotation/rotation rate/rotation acceleration triplet.

Parameters:

rotation - rotation

rotationRate - rotation rate Ω (rad/s)

rotationAcceleration - rotation acceleration dΩ/dt (rad²/s²)

AngularCoordinates

public AngularCoordinates(PVCoordinates u1,
                  PVCoordinates u2,
                  PVCoordinates v1,
                  PVCoordinates v2,
                  double tolerance)
                   throws OrekitException

Build the rotation that transforms a pair of pv coordinates into another one.

WARNING! This method requires much more stringent assumptions on its parameters than the similar constructor from the Rotation class. As far as the Rotation constructor is concerned, the v₂ vector from the second pair can be slightly misaligned. The Rotation constructor will compensate for this misalignment and create a rotation that ensure v₁ = r(u₁) and v₂ ∈ plane (r(u₁), r(u₂)). THIS IS NOT TRUE ANYMORE IN THIS CLASS! As derivatives are involved and must be preserved, this constructor works only if the two pairs are fully consistent, i.e. if a rotation exists that fulfill all the requirements: v₁ = r(u₁), v₂ = r(u₂), dv₁/dt = dr(u₁)/dt, dv₂/dt = dr(u₂)/dt, d²v₁/dt² = d²r(u₁)/dt², d²v₂/dt² = d²r(u₂)/dt².

Parameters:

u1 - first vector of the origin pair

u2 - second vector of the origin pair

v1 - desired image of u1 by the rotation

v2 - desired image of u2 by the rotation

tolerance - relative tolerance factor used to check singularities

Throws:

OrekitException - if the vectors are inconsistent for the rotation to be found (null, aligned, ...)

AngularCoordinates

public AngularCoordinates(PVCoordinates u,
                  PVCoordinates v)
                   throws OrekitException

Build one of the rotations that transform one pv coordinates into another one.

Except for a possible scale factor, if the instance were applied to the vector u it will produce the vector v. There is an infinite number of such rotations, this constructor choose the one with the smallest associated angle (i.e. the one whose axis is orthogonal to the (u, v) plane). If u and v are collinear, an arbitrary rotation axis is chosen.

Parameters:

u - origin vector

v - desired image of u by the rotation

Throws:

OrekitException - if the vectors components cannot be converted to DerivativeStructure with proper order

AngularCoordinates

public AngularCoordinates(FieldRotation<DerivativeStructure> r)

Builds a AngularCoordinates from a FieldRotation<DerivativeStructure>.

The rotation components must have time as their only derivation parameter and have consistent derivation orders.

Parameters:

r - rotation with time-derivatives embedded within the coordinates

Method Detail

toDerivativeStructureRotation

public FieldRotation<DerivativeStructure> toDerivativeStructureRotation(int order)
                                                                 throws OrekitException

Transform the instance to a FieldRotation<DerivativeStructure>.

The DerivativeStructure coordinates correspond to time-derivatives up to the user-specified order.

Parameters:

order - derivation order for the vector components

Returns:

rotation with time-derivatives embedded within the coordinates

Throws:

OrekitException - if the user specified order is too large

estimateRate

public static Vector3D estimateRate(Rotation start,
                    Rotation end,
                    double dt)

Estimate rotation rate between two orientations.

Estimation is based on a simple fixed rate rotation during the time interval between the two orientations.

Parameters:

start - start orientation

end - end orientation

dt - time elapsed between the dates of the two orientations

Returns:

rotation rate allowing to go from start to end orientations

revert

public AngularCoordinates revert()

Revert a rotation/rotation rate/ rotation acceleration triplet. Build a triplet which reverse the effect of another triplet.

Returns:

a new triplet whose effect is the reverse of the effect of the instance

shiftedBy

public AngularCoordinates shiftedBy(double dt)

Get a time-shifted state.

The state can be slightly shifted to close dates. This shift is based on an approximate solution of the fixed acceleration motion. It is not intended as a replacement for proper attitude propagation but should be sufficient for either small time shifts or coarse accuracy.

Specified by:

shiftedBy in interface TimeShiftable<AngularCoordinates>

Parameters:

dt - time shift in seconds

Returns:

a new state, shifted with respect to the instance (which is immutable)

getRotation

public Rotation getRotation()

Get the rotation.

Returns:

the rotation.

getRotationRate

public Vector3D getRotationRate()

Get the rotation rate.

Returns:

the rotation rate vector Ω (rad/s).

getRotationAcceleration

public Vector3D getRotationAcceleration()

Get the rotation acceleration.

Returns:

the rotation acceleration vector dΩ/dt (rad²/s²).

addOffset

public AngularCoordinates addOffset(AngularCoordinates offset)

Add an offset from the instance.

We consider here that the offset rotation is applied first and the instance is applied afterward. Note that angular coordinates do not commute under this operation, i.e. a.addOffset(b) and b.addOffset(a) lead to different results in most cases.

The two methods addOffset and subtractOffset are designed so that round trip applications are possible. This means that both ac1.subtractOffset(ac2).addOffset(ac2) and ac1.addOffset(ac2).subtractOffset(ac2) return angular coordinates equal to ac1.

Parameters:

offset - offset to subtract

Returns:

new instance, with offset subtracted

See Also:

subtractOffset(AngularCoordinates)

subtractOffset

public AngularCoordinates subtractOffset(AngularCoordinates offset)

Subtract an offset from the instance.

We consider here that the offset rotation is applied first and the instance is applied afterward. Note that angular coordinates do not commute under this operation, i.e. a.subtractOffset(b) and b.subtractOffset(a) lead to different results in most cases.

The two methods addOffset and subtractOffset are designed so that round trip applications are possible. This means that both ac1.subtractOffset(ac2).addOffset(ac2) and ac1.addOffset(ac2).subtractOffset(ac2) return angular coordinates equal to ac1.

Parameters:

offset - offset to subtract

Returns:

new instance, with offset subtracted

See Also:

addOffset(AngularCoordinates)

applyTo

public PVCoordinates applyTo(PVCoordinates pv)

Apply the rotation to a pv coordinates.

Parameters:

pv - vector to apply the rotation to

Returns:

a new pv coordinates which is the image of u by the rotation

applyTo

public TimeStampedPVCoordinates applyTo(TimeStampedPVCoordinates pv)

Apply the rotation to a pv coordinates.

Parameters:

pv - vector to apply the rotation to

Returns:

a new pv coordinates which is the image of u by the rotation

interpolate

@Deprecated
public static AngularCoordinates interpolate(AbsoluteDate date,
                                        boolean useRotationRates,
                                        Collection<Pair<AbsoluteDate,AngularCoordinates>> sample)
                                      throws OrekitException

Deprecated. since 7.0 replaced with TimeStampedAngularCoordinates.interpolate(AbsoluteDate, AngularDerivativesFilter, Collection)

Interpolate angular coordinates.

The interpolated instance is created by polynomial Hermite interpolation on Rodrigues vector ensuring rotation rate remains the exact derivative of rotation.

This method is based on Sergei Tanygin's paper Attitude Interpolation, changing the norm of the vector to match the modified Rodrigues vector as described in Malcolm D. Shuster's paper A Survey of Attitude Representations. This change avoids the singularity at π. There is still a singularity at 2π, which is handled by slightly offsetting all rotations when this singularity is detected.

Note that even if first time derivatives (rotation rates) 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 rotations.

Parameters:

date - interpolation date

useRotationRates - if true, use sample points rotation rates, otherwise ignore them and use only rotations

sample - sample points on which interpolation should be done

Returns:

a new position-velocity, interpolated at specified date

Throws:

OrekitException - if the number of point is too small for interpolating

getModifiedRodrigues

public double[][] getModifiedRodrigues(double sign)

Convert rotation, rate and acceleration to modified Rodrigues vector and derivatives.

The modified Rodrigues vector is tan(θ/4) u where θ and u are the rotation angle and axis respectively.

Parameters:

sign - multiplicative sign for quaternion components

Returns:

modified Rodrigues vector and derivatives (vector on row 0, first derivative on row 1, second derivative on row 2)

See Also:

createFromModifiedRodrigues(double[][])

createFromModifiedRodrigues

public static AngularCoordinates createFromModifiedRodrigues(double[][] r)

Convert a modified Rodrigues vector and derivatives to angular coordinates.

Parameters:

r - modified Rodrigues vector (with first and second times derivatives)

Returns:

angular coordinates

See Also:

getModifiedRodrigues(double)