T - the type of the field elementspublic class TimeStampedFieldAngularCoordinates<T extends RealFieldElement<T>> extends FieldAngularCoordinates<T>
time-stamped version of FieldAngularCoordinates.
Instances of this class are guaranteed to be immutable.
applyTo, applyTo, applyTo, applyTo, createFromModifiedRodrigues, estimateRate, estimateRate, getIdentity, getModifiedRodrigues, getRotation, getRotationAcceleration, getRotationRate, toAngularCoordinates, toDerivativeStructureRotationpublic TimeStampedFieldAngularCoordinates(AbsoluteDate date, FieldPVCoordinates<T> u1, FieldPVCoordinates<T> u2, FieldPVCoordinates<T> v1, FieldPVCoordinates<T> v2, double tolerance)
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.
date - coordinates dateu1 - first vector of the origin pairu2 - second vector of the origin pairv1 - desired image of u1 by the rotationv2 - desired image of u2 by the rotationtolerance - relative tolerance factor used to check singularitiespublic TimeStampedFieldAngularCoordinates(FieldAbsoluteDate<T> date, FieldPVCoordinates<T> u1, FieldPVCoordinates<T> u2, FieldPVCoordinates<T> v1, FieldPVCoordinates<T> v2, double tolerance)
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.
date - coordinates dateu1 - first vector of the origin pairu2 - second vector of the origin pairv1 - desired image of u1 by the rotationv2 - desired image of u2 by the rotationtolerance - relative tolerance factor used to check singularitiespublic TimeStampedFieldAngularCoordinates(AbsoluteDate date, FieldRotation<T> rotation, FieldVector3D<T> rotationRate, FieldVector3D<T> rotationAcceleration)
date - coordinates daterotation - rotationrotationRate - rotation rate Ω (rad/s)rotationAcceleration - rotation acceleration dΩ/dt (rad²/s²)public TimeStampedFieldAngularCoordinates(FieldAbsoluteDate<T> date, FieldRotation<T> rotation, FieldVector3D<T> rotationRate, FieldVector3D<T> rotationAcceleration)
date - coordinates daterotation - rotationrotationRate - rotation rate Ω (rad/s)rotationAcceleration - rotation acceleration dΩ/dt (rad²/s²)public TimeStampedFieldAngularCoordinates(Field<T> field, TimeStampedAngularCoordinates ac)
TimeStampedAngularCoordinates.field - fields to which the elements belongac - coordinates to convertpublic TimeStampedFieldAngularCoordinates(FieldAbsoluteDate<T> date, FieldRotation<FieldDerivativeStructure<T>> r)
FieldRotation<FieldDerivativeStructure>.
The rotation components must have time as their only derivation parameter and have consistent derivation orders.
date - coordinates dater - rotation with time-derivatives embedded within the coordinatespublic TimeStampedFieldAngularCoordinates<T> revert()
revert in class FieldAngularCoordinates<T extends RealFieldElement<T>>public FieldAbsoluteDate<T> getDate()
public TimeStampedFieldAngularCoordinates<T> shiftedBy(double dt)
The state can be slightly shifted to close dates. This shift is based on a simple linear model. It is not intended as a replacement for proper attitude propagation but should be sufficient for either small time shifts or coarse accuracy.
shiftedBy in class FieldAngularCoordinates<T extends RealFieldElement<T>>dt - time shift in secondspublic TimeStampedFieldAngularCoordinates<T> shiftedBy(T dt)
The state can be slightly shifted to close dates. This shift is based on a simple linear model. It is not intended as a replacement for proper attitude propagation but should be sufficient for either small time shifts or coarse accuracy.
shiftedBy in class FieldAngularCoordinates<T extends RealFieldElement<T>>dt - time shift in secondspublic TimeStampedFieldAngularCoordinates<T> addOffset(FieldAngularCoordinates<T> offset)
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.
addOffset in class FieldAngularCoordinates<T extends RealFieldElement<T>>offset - offset to subtractsubtractOffset(FieldAngularCoordinates)public TimeStampedFieldAngularCoordinates<T> subtractOffset(FieldAngularCoordinates<T> offset)
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.
subtractOffset in class FieldAngularCoordinates<T extends RealFieldElement<T>>offset - offset to subtractaddOffset(FieldAngularCoordinates)public static <T extends RealFieldElement<T>> TimeStampedFieldAngularCoordinates<T> interpolate(AbsoluteDate date, AngularDerivativesFilter filter, Collection<TimeStampedFieldAngularCoordinates<T>> sample)
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.
T - the type of the field elementsdate - interpolation datefilter - filter for derivatives from the sample to use in interpolationsample - sample points on which interpolation should be donepublic static <T extends RealFieldElement<T>> TimeStampedFieldAngularCoordinates<T> interpolate(FieldAbsoluteDate<T> date, AngularDerivativesFilter filter, Collection<TimeStampedFieldAngularCoordinates<T>> sample)
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.
T - the type of the field elementsdate - interpolation datefilter - filter for derivatives from the sample to use in interpolationsample - sample points on which interpolation should be doneCopyright © 2002-2020 CS Group. All rights reserved.