Package org.orekit.utils

Class 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 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 (rad/s²)

      • AngularCoordinates

        public AngularCoordinates​(Rotation rotation)
        Builds angular coordinates with the given rotation, zero angular velocity, and zero angular acceleration.
        Parameters:
        rotation - rotation

      • 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<U> r)
        Builds a AngularCoordinates from a FieldRotation<Derivative>.

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

        Type Parameters:
        U - type of the derivative
        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

      • rotationShiftedBy

        public Rotation rotationShiftedBy​(double dt)
        Get a time-shifted rotation. Same as shiftedBy(double) except only the shifted rotation is computed.

        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.

        Parameters:
        dt - time shift in seconds
        Returns:
        a new state, shifted with respect to the instance (which is immutable)
        See Also:
        shiftedBy(double)

      • 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 (rad/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 pv 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 pv by the rotation

      • applyTo

        public <T extends CalculusFieldElement<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 pv 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)