AngularCoordinates (ORbit Extrapolation KIT 10.0 API)

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).

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

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`AngularCoordinates`	`addOffset(AngularCoordinates offset)` Add an offset from the instance.
`<T extends RealFieldElement<T>> FieldPVCoordinates<T>`	`applyTo(FieldPVCoordinates<T> pv)` Apply the rotation to a pv coordinates.
`PVCoordinates`	`applyTo(PVCoordinates pv)` Apply the rotation to a pv coordinates.
`<T extends RealFieldElement<T>> TimeStampedFieldPVCoordinates<T>`	`applyTo(TimeStampedFieldPVCoordinates<T> 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.
`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)
```
    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
  - AngularCoordinates
```
public AngularCoordinates(PVCoordinates u,
                          PVCoordinates v)
```
    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
  - 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)
```
    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
  - 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
  - applyTo
```
public <T extends RealFieldElement<T>> FieldPVCoordinates<T> applyTo(FieldPVCoordinates<T> pv)
```
    Apply the rotation to a pv coordinates.
    
    Type Parameters:
    
    T - type of the field elements
    
    Parameters:
    
    pv - vector to apply the rotation to
    
    Returns:
    
    a new pv coordinates which is the image of u by the rotation
    
    Since:
    
    9.0
  - applyTo
```
public <T extends RealFieldElement<T>> TimeStampedFieldPVCoordinates<T> applyTo(TimeStampedFieldPVCoordinates<T> pv)
```
    Apply the rotation to a pv coordinates.
    
    Type Parameters:
    
    T - type of the field elements
    
    Parameters:
    
    pv - vector to apply the rotation to
    
    Returns:
    
    a new pv coordinates which is the image of u by the rotation
    
    Since:
    
    9.0
  - 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)

Class AngularCoordinates

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

IDENTITY

Constructor Detail

AngularCoordinates

AngularCoordinates

AngularCoordinates

AngularCoordinates

AngularCoordinates

AngularCoordinates

Method Detail

toDerivativeStructureRotation

estimateRate

revert

shiftedBy

getRotation

getRotationRate

getRotationAcceleration

addOffset

subtractOffset

applyTo

applyTo

applyTo

applyTo

getModifiedRodrigues

createFromModifiedRodrigues