Package org.orekit.utils

Class TimeStampedAngularCoordinatesHermiteInterpolator

java.lang.Object

org.orekit.time.AbstractTimeInterpolator<TimeStampedAngularCoordinates>

org.orekit.utils.TimeStampedAngularCoordinatesHermiteInterpolator

All Implemented Interfaces:

TimeInterpolator<TimeStampedAngularCoordinates>

public class TimeStampedAngularCoordinatesHermiteInterpolator
extends AbstractTimeInterpolator<TimeStampedAngularCoordinates>

Class using Hermite interpolator to interpolate time stamped angular coordinates.

As this implementation of interpolation is polynomial, it should be used only with small number of interpolation points (about 10-20 points) in order to avoid Runge's phenomenon and numerical problems (including NaN appearing).

Author:

Vincent Cucchietti, Luc Maisonobe

See Also:

HermiteInterpolator, TimeStampedAngularCoordinates

Nested Class Summary

Nested classes/interfaces inherited from class org.orekit.time.AbstractTimeInterpolator

AbstractTimeInterpolator.InterpolationData

Field Summary

Fields inherited from class org.orekit.time.AbstractTimeInterpolator

DEFAULT_EXTRAPOLATION_THRESHOLD_SEC, DEFAULT_INTERPOLATION_POINTS

Constructor Summary

Constructors

Constructor	Description
TimeStampedAngularCoordinatesHermiteInterpolator()	Constructor with : Default number of interpolation points of DEFAULT_INTERPOLATION_POINTS Default extrapolation threshold value (DEFAULT_EXTRAPOLATION_THRESHOLD_SEC s) Use of angular and first time derivative for attitude interpolation As this implementation of interpolation is polynomial, it should be used only with small number of interpolation points (about 10-20 points) in order to avoid Runge's phenomenon and numerical problems (including NaN appearing).
TimeStampedAngularCoordinatesHermiteInterpolator(int interpolationPoints)	/** Constructor with : Default extrapolation threshold value (DEFAULT_EXTRAPOLATION_THRESHOLD_SEC s) Use of angular and first time derivative for attitude interpolation As this implementation of interpolation is polynomial, it should be used only with small number of interpolation points (about 10-20 points) in order to avoid Runge's phenomenon and numerical problems (including NaN appearing).
TimeStampedAngularCoordinatesHermiteInterpolator(int interpolationPoints, double extrapolationThreshold, AngularDerivativesFilter filter)	Constructor.
TimeStampedAngularCoordinatesHermiteInterpolator(int interpolationPoints, AngularDerivativesFilter filter)	Constructor with : Default extrapolation threshold value (DEFAULT_EXTRAPOLATION_THRESHOLD_SEC s) As this implementation of interpolation is polynomial, it should be used only with small number of interpolation points (about 10-20 points) in order to avoid Runge's phenomenon and numerical problems (including NaN appearing).

Method Summary

Modifier and Type	Method	Description
AngularDerivativesFilter	getFilter()	Get filter for derivatives from the sample to use in interpolation.
protected TimeStampedAngularCoordinates	interpolate(AbstractTimeInterpolator.InterpolationData interpolationData)	Interpolate instance from given interpolation data.

Methods inherited from class org.orekit.time.AbstractTimeInterpolator

addOptionalSubInterpolatorIfDefined, checkInterpolatorCompatibilityWithSampleSize, getCentralDate, getCentralDate, getExtrapolationThreshold, getNbInterpolationPoints, getSubInterpolators, getTimeParameter, interpolate, interpolate

Methods inherited from class java.lang.Object

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

Constructor Detail

TimeStampedAngularCoordinatesHermiteInterpolator

public TimeStampedAngularCoordinatesHermiteInterpolator()

Constructor with :

• Default number of interpolation points of DEFAULT_INTERPOLATION_POINTS
• Default extrapolation threshold value (DEFAULT_EXTRAPOLATION_THRESHOLD_SEC s)
• Use of angular and first time derivative for attitude interpolation

As this implementation of interpolation is polynomial, it should be used only with small number of interpolation points (about 10-20 points) in order to avoid Runge's phenomenon and numerical problems (including NaN appearing).

TimeStampedAngularCoordinatesHermiteInterpolator

public TimeStampedAngularCoordinatesHermiteInterpolator(int interpolationPoints)

/** Constructor with :

• Default extrapolation threshold value (DEFAULT_EXTRAPOLATION_THRESHOLD_SEC s)
• Use of angular and first time derivative for attitude interpolation

As this implementation of interpolation is polynomial, it should be used only with small number of interpolation points (about 10-20 points) in order to avoid Runge's phenomenon and numerical problems (including NaN appearing).

Parameters:

interpolationPoints - number of interpolation points

TimeStampedAngularCoordinatesHermiteInterpolator

public TimeStampedAngularCoordinatesHermiteInterpolator(int interpolationPoints,
                                                        AngularDerivativesFilter filter)

Constructor with :

• Default extrapolation threshold value (DEFAULT_EXTRAPOLATION_THRESHOLD_SEC s)

As this implementation of interpolation is polynomial, it should be used only with small number of interpolation points (about 10-20 points) in order to avoid Runge's phenomenon and numerical problems (including NaN appearing).

Parameters:

interpolationPoints - number of interpolation points

filter - filter for derivatives from the sample to use in interpolation

TimeStampedAngularCoordinatesHermiteInterpolator

public TimeStampedAngularCoordinatesHermiteInterpolator(int interpolationPoints,
                                                        double extrapolationThreshold,
                                                        AngularDerivativesFilter filter)

Constructor.

As this implementation of interpolation is polynomial, it should be used only with small number of interpolation points (about 10-20 points) in order to avoid Runge's phenomenon and numerical problems (including NaN appearing).

Parameters:

interpolationPoints - number of interpolation points

extrapolationThreshold - extrapolation threshold beyond which the propagation will fail

filter - filter for derivatives from the sample to use in interpolation

Method Detail

getFilter

public AngularDerivativesFilter getFilter()

Get filter for derivatives from the sample to use in interpolation.

Returns:

filter for derivatives from the sample to use in interpolation

interpolate

protected TimeStampedAngularCoordinates interpolate(AbstractTimeInterpolator.InterpolationData interpolationData)

Interpolate instance from given interpolation data.

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.

Specified by:

interpolate in class AbstractTimeInterpolator<TimeStampedAngularCoordinates>

Parameters:

interpolationData - interpolation data

Returns:

interpolated instance from given interpolation data.