fr.cnes.sirius.patrius.orbits

Class KeplerianOrbit

java.lang.Object

fr.cnes.sirius.patrius.orbits.Orbit

fr.cnes.sirius.patrius.orbits.KeplerianOrbit

All Implemented Interfaces:

PVCoordinatesProvider, TimeInterpolable<Orbit>, TimeShiftable<Orbit>, TimeStamped, Serializable

public final class KeplerianOrbit
extends Orbit

This class handles traditional keplerian orbital parameters.

The parameters used internally are the keplerian elements (see KeplerianParameters for more information.

The instance KeplerianOrbit is guaranteed to be immutable.

Author:

Luc Maisonobe, Guylaine Prat, Fabien Maussion, Véronique Pommier-Maurussane

See Also:

Orbit, CircularOrbit, CartesianOrbit, EquinoctialOrbit, Serialized Form

Constructor Summary

Constructors

Constructor and Description
KeplerianOrbit(double a, double e, double i, double pa, double raan, double anomaly, PositionAngle type, Frame frame, AbsoluteDate date, double mu) Creates a new instance.
KeplerianOrbit(IOrbitalParameters parametersIn, Frame frame, AbsoluteDate date) Creates a new instance.
KeplerianOrbit(Orbit op) Constructor from any kind of orbital parameters.
KeplerianOrbit(PVCoordinates pvCoordinates, Frame frame, AbsoluteDate date, double mu) Constructor from cartesian parameters.

Method Summary

Modifier and Type	Method and Description
protected double[][]	computeJacobianEccentricWrtCartesian() Compute the Jacobian of the orbital parameters with eccentric angle with respect to the Cartesian parameters.
protected double[][]	computeJacobianMeanWrtCartesian() Compute the Jacobian of the orbital parameters with mean angle with respect to the Cartesian parameters.
protected double[][]	computeJacobianTrueWrtCartesian() Compute the Jacobian of the orbital parameters with true angle with respect to the Cartesian parameters.
double	getA() Get the semi-major axis.
double	getAnomaly(PositionAngle type) Get the anomaly.
double	getE() Get the eccentricity.
double	getEccentricAnomaly() Get the eccentric anomaly.
double	getEquinoctialEx() Get the first component of the equinoctial eccentricity vector.
double	getEquinoctialEy() Get the second component of the equinoctial eccentricity vector.
double	getHx() Get hx = ix / (2 * cos(i/2)), where ix is the first component of the inclination vector.
double	getHy() Get hy = iy / (2 * cos(i/2)), where iy is the second component of the inclination vector.
double	getI() Get the inclination.
KeplerianParameters	getKeplerianParameters() Getter for underlying keplerian parameters.
double	getLE() Get the eccentric longitude argument.
double	getLM() Get the mean longitude argument.
double	getLv() Get the true longitude argument.
double	getMeanAnomaly() Get the mean anomaly.
IOrbitalParameters	getParameters() Get underlying orbital parameters.
double	getPerigeeArgument() Get the perigee argument.
double	getRightAscensionOfAscendingNode() Get the right ascension of the ascending node.
double	getTrueAnomaly() Get the true anomaly.
OrbitType	getType() Get the orbit type.
protected PVCoordinates	initPVCoordinates() Compute the position/velocity coordinates from the canonical parameters.
KeplerianOrbit	interpolate(AbsoluteDate date, Collection<Orbit> sample) Get an interpolated instance.
protected void	orbitAddKeplerContribution(PositionAngle type, double gm, double[] pDot) Add the contribution of the Keplerian motion to parameters derivatives
protected KeplerianOrbit	orbitShiftedBy(double dt) Get a time-shifted orbit.
String	toString()

Methods inherited from class fr.cnes.sirius.patrius.orbits.Orbit

addKeplerContribution, createInverseJacobian, fillHalfRow, fillHalfRow, fillHalfRow, fillHalfRow, fillHalfRow, fillHalfRow, getDate, getFrame, getJacobian, getJacobianWrtCartesian, getJacobianWrtParameters, getJacobianWrtParametersEccentric, getJacobianWrtParametersMean, getJacobianWrtParametersTrue, getKeplerianMeanMotion, getKeplerianPeriod, getKeplerianTransitionMatrix, getMu, getPVCoordinates, getPVCoordinates, getPVCoordinates, isPositiveDefinite, setJacobianWrtParametersEccentric, setJacobianWrtParametersMean, setJacobianWrtParametersTrue, shiftedBy

Methods inherited from class java.lang.Object

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

Constructor Detail

KeplerianOrbit

public KeplerianOrbit(IOrbitalParameters parametersIn,
                      Frame frame,
                      AbsoluteDate date)

Creates a new instance.

Parameters:

parametersIn - orbital parameters

frame - the frame in which the parameters are defined

date - date of the orbital parameters

KeplerianOrbit

public KeplerianOrbit(double a,
                      double e,
                      double i,
                      double pa,
                      double raan,
                      double anomaly,
                      PositionAngle type,
                      Frame frame,
                      AbsoluteDate date,
                      double mu)

Creates a new instance.

Parameters:

a - semi-major axis (m), negative for hyperbolic orbits

e - eccentricity (e >= 0)

i - inclination (rad)

pa - perigee argument (ω, rad)

raan - right ascension of ascending node (Ω, rad)

anomaly - mean, eccentric or true anomaly (rad)

type - type of anomaly

frame - the frame in which the parameters are defined

date - date of the orbital parameters

mu - central attraction coefficient (m³/s²)

Throws:

IllegalArgumentException - if a and e don't match for hyperbolic orbits, or v is out of range for hyperbolic orbits

KeplerianOrbit

public KeplerianOrbit(PVCoordinates pvCoordinates,
                      Frame frame,
                      AbsoluteDate date,
                      double mu)

Constructor from cartesian parameters.

Parameters:

pvCoordinates - the PVCoordinates of the satellite

frame - the frame in which are defined the PVCoordinates

date - date of the orbital parameters

mu - central attraction coefficient (m³/s²)

KeplerianOrbit

public KeplerianOrbit(Orbit op)

Constructor from any kind of orbital parameters.

Parameters:

op - orbital parameters to copy

Method Detail

getParameters

public IOrbitalParameters getParameters()

Get underlying orbital parameters.

Specified by:

getParameters in class Orbit

Returns:

orbital parameters

getKeplerianParameters

public KeplerianParameters getKeplerianParameters()

Getter for underlying keplerian parameters.

Returns:

keplerian parameters

getType

public OrbitType getType()

Get the orbit type.

Specified by:

getType in class Orbit

Returns:

orbit type

getA

public double getA()

Get the semi-major axis.

Note that the semi-major axis is considered negative for hyperbolic orbits.

Specified by:

getA in class Orbit

Returns:

semi-major axis (m)

getE

public double getE()

Get the eccentricity.

Specified by:

getE in class Orbit

Returns:

eccentricity

getI

public double getI()

Get the inclination.

Specified by:

getI in class Orbit

Returns:

inclination (rad)

getPerigeeArgument

public double getPerigeeArgument()

Get the perigee argument.

Returns:

perigee argument (rad)

getRightAscensionOfAscendingNode

public double getRightAscensionOfAscendingNode()

Get the right ascension of the ascending node.

Returns:

right ascension of the ascending node (rad)

getAnomaly

public double getAnomaly(PositionAngle type)

Get the anomaly.

Parameters:

type - type of the angle

Returns:

anomaly (rad)

getTrueAnomaly

public double getTrueAnomaly()

Get the true anomaly.

Returns:

true anomaly (rad)

getEccentricAnomaly

public double getEccentricAnomaly()

Get the eccentric anomaly.

Returns:

eccentric anomaly (rad)

getMeanAnomaly

public double getMeanAnomaly()

Get the mean anomaly.

Returns:

mean anomaly (rad)

getEquinoctialEx

public double getEquinoctialEx()

Get the first component of the equinoctial eccentricity vector.

Specified by:

getEquinoctialEx in class Orbit

Returns:

first component of the equinoctial eccentricity vector

getEquinoctialEy

public double getEquinoctialEy()

Get the second component of the equinoctial eccentricity vector.

Specified by:

getEquinoctialEy in class Orbit

Returns:

second component of the equinoctial eccentricity vector

getHx

public double getHx()

Get hx = ix / (2 * cos(i/2)), where ix is the first component of the inclination vector. Another formulation is hx = tan(i/2) cos(Ω)

Specified by:

getHx in class Orbit

Returns:

first component of the inclination vector

getHy

public double getHy()

Get hy = iy / (2 * cos(i/2)), where iy is the second component of the inclination vector. Another formulation is hy = tan(i/2) sin(Ω)

Specified by:

getHy in class Orbit

Returns:

second component of the inclination vector

getLv

public double getLv()

Get the true longitude argument.

Specified by:

getLv in class Orbit

Returns:

true longitude argument (rad)

getLE

public double getLE()

Get the eccentric longitude argument.

Specified by:

getLE in class Orbit

Returns:

eccentric longitude argument (rad)

getLM

public double getLM()

Get the mean longitude argument.

Specified by:

getLM in class Orbit

Returns:

mean longitude argument (rad)

initPVCoordinates

protected PVCoordinates initPVCoordinates()

Compute the position/velocity coordinates from the canonical parameters.

Specified by:

initPVCoordinates in class Orbit

Returns:

computed position/velocity coordinates

orbitShiftedBy

protected KeplerianOrbit orbitShiftedBy(double dt)

Get a time-shifted orbit.

The orbit can be slightly shifted to close dates. This shift is based on a simple keplerian model. It is not intended as a replacement for proper orbit and attitude propagation but should be sufficient for small time shifts or coarse accuracy.

Specified by:

orbitShiftedBy in class Orbit

Parameters:

dt - time shift in seconds

Returns:

a new orbit, shifted with respect to the instance (which is immutable)

interpolate

public KeplerianOrbit interpolate(AbsoluteDate date,
                                  Collection<Orbit> sample)

Get an interpolated instance.

Note that the state of the current instance may not be used in the interpolation process, only its type and non interpolable fields are used (for example central attraction coefficient or frame when interpolating orbits). The interpolable fields taken into account are taken only from the states of the sample points. So if the state of the instance must be used, the instance should be included in the sample points.

The interpolated instance is created by polynomial Hermite interpolation on Keplerian elements, without derivatives (which means the interpolation falls back to Lagrange interpolation only).

Parameters:

date - interpolation date

sample - sample points on which interpolation should be done

Returns:

a new instance, interpolated at specified date

computeJacobianMeanWrtCartesian

protected double[][] computeJacobianMeanWrtCartesian()

Compute the Jacobian of the orbital parameters with mean angle with respect to the Cartesian parameters.

Element jacobian[i][j] is the derivative of parameter i of the orbit with respect to Cartesian coordinate j. This means each row correspond to one orbital parameter whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.

Specified by:

computeJacobianMeanWrtCartesian in class Orbit

Returns:

6x6 Jacobian matrix

See Also:

Orbit.computeJacobianEccentricWrtCartesian(), Orbit.computeJacobianTrueWrtCartesian()

computeJacobianEccentricWrtCartesian

protected double[][] computeJacobianEccentricWrtCartesian()

Compute the Jacobian of the orbital parameters with eccentric angle with respect to the Cartesian parameters.

Element jacobian[i][j] is the derivative of parameter i of the orbit with respect to Cartesian coordinate j. This means each row correspond to one orbital parameter whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.

Specified by:

computeJacobianEccentricWrtCartesian in class Orbit

Returns:

6x6 Jacobian matrix

See Also:

Orbit.computeJacobianMeanWrtCartesian(), Orbit.computeJacobianTrueWrtCartesian()

computeJacobianTrueWrtCartesian

protected double[][] computeJacobianTrueWrtCartesian()

Compute the Jacobian of the orbital parameters with true angle with respect to the Cartesian parameters.

Element jacobian[i][j] is the derivative of parameter i of the orbit with respect to Cartesian coordinate j. This means each row correspond to one orbital parameter whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.

Specified by:

computeJacobianTrueWrtCartesian in class Orbit

Returns:

6x6 Jacobian matrix

See Also:

Orbit.computeJacobianMeanWrtCartesian(), Orbit.computeJacobianEccentricWrtCartesian()

orbitAddKeplerContribution

protected void orbitAddKeplerContribution(PositionAngle type,
                                          double gm,
                                          double[] pDot)

Add the contribution of the Keplerian motion to parameters derivatives

This method is used by numerical propagators to evaluate the part of Keplerrian motion to evolution of the orbital state.

Specified by:

orbitAddKeplerContribution in class Orbit

Parameters:

type - type of the position angle in the state

gm - attraction coefficient to use

pDot - array containing orbital state derivatives to update (the Keplerian part must be added to the array components, as the array may already contain some non-zero elements corresponding to non-Keplerian parts)

toString

public String toString()

Overrides:

toString in class Object