Package org.orekit.utils

Class TimeStampedAngularCoordinates

    • Constructor Detail

      • TimeStampedAngularCoordinates

        public TimeStampedAngularCoordinates​(AbsoluteDate date,
                                     org.hipparchus.geometry.euclidean.threed.Rotation rotation,
                                     org.hipparchus.geometry.euclidean.threed.Vector3D rotationRate,
                                     org.hipparchus.geometry.euclidean.threed.Vector3D rotationAcceleration)
        Builds a rotation/rotation rate pair.
        Parameters:
        date - coordinates date
        rotation - rotation
        rotationRate - rotation rate Ω (rad/s)
        rotationAcceleration - rotation acceleration dΩ/dt (rad²/s²)

      • TimeStampedAngularCoordinates

        public TimeStampedAngularCoordinates​(AbsoluteDate date,
                                     PVCoordinates u1,
                                     PVCoordinates u2,
                                     PVCoordinates v1,
                                     PVCoordinates v2,
                                     double tolerance)
        Build the rotation that transforms a pair of pv coordinates into another pair.

        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:
        date - coordinates date
        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

      • TimeStampedAngularCoordinates

        public TimeStampedAngularCoordinates​(AbsoluteDate date,
                                     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:
        date - coordinates date
        u - origin vector
        v - desired image of u by the rotation

      • TimeStampedAngularCoordinates

        public TimeStampedAngularCoordinates​(AbsoluteDate date,
                                     org.hipparchus.geometry.euclidean.threed.FieldRotation<org.hipparchus.analysis.differentiation.DerivativeStructure> r)
        Builds a TimeStampedAngularCoordinates from a FieldRotation<DerivativeStructure>.

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

        Parameters:
        date - coordinates date
        r - rotation with time-derivatives embedded within the coordinates

    • Method Detail

      • revert

        public TimeStampedAngularCoordinates revert()
        Revert a rotation/rotation rate pair. Build a pair which reverse the effect of another pair.
        Overrides:
        revert in class AngularCoordinates
        Returns:
        a new pair whose effect is the reverse of the effect of the instance

      • shiftedBy

        public TimeStampedAngularCoordinates shiftedBy​(double dt)
        Get a time-shifted state.

        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.

        Specified by:
        shiftedBy in interface TimeShiftable<AngularCoordinates>
        Overrides:
        shiftedBy in class AngularCoordinates
        Parameters:
        dt - time shift in seconds
        Returns:
        a new state, shifted with respect to the instance (which is immutable)

      • addOffset

        public TimeStampedAngularCoordinates 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.

        Overrides:
        addOffset in class AngularCoordinates
        Parameters:
        offset - offset to subtract
        Returns:
        new instance, with offset subtracted
        See Also:
        subtractOffset(AngularCoordinates)

      • subtractOffset

        public TimeStampedAngularCoordinates 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.

        Overrides:
        subtractOffset in class AngularCoordinates
        Parameters:
        offset - offset to subtract
        Returns:
        new instance, with offset subtracted
        See Also:
        addOffset(AngularCoordinates)

      • interpolate

        public static TimeStampedAngularCoordinates interpolate​(AbsoluteDate date,
                                                        AngularDerivativesFilter filter,
                                                        Collection<TimeStampedAngularCoordinates> sample)
        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. Another change is that the mean linear motion is first removed before interpolation and added back after interpolation. This allows to use interpolation even when the sample covers much more than one turn and even when sample points are separated by more than one turn.

        Note that even if first and second time derivatives (rotation rates and acceleration) 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
        filter - filter for derivatives from the sample to use in interpolation
        sample - sample points on which interpolation should be done
        Returns:
        a new position-velocity, interpolated at specified date