Package org.orekit.orbits

Class EquinoctialOrbit

java.lang.Object

org.orekit.orbits.Orbit

org.orekit.orbits.EquinoctialOrbit

All Implemented Interfaces:

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

public class EquinoctialOrbit
extends Orbit

This class handles equinoctial orbital parameters, which can support both circular and equatorial orbits.

The parameters used internally are the equinoctial elements which can be related to Keplerian elements as follows:

     a
     ex = e cos(ω + Ω)
     ey = e sin(ω + Ω)
     hx = tan(i/2) cos(Ω)
     hy = tan(i/2) sin(Ω)
     lv = v + ω + Ω
   

where ω stands for the Perigee Argument and Ω stands for the Right Ascension of the Ascending Node.

The conversion equations from and to Keplerian elements given above hold only when both sides are unambiguously defined, i.e. when orbit is neither equatorial nor circular. When orbit is either equatorial or circular, the equinoctial parameters are still unambiguously defined whereas some Keplerian elements (more precisely ω and Ω) become ambiguous. For this reason, equinoctial parameters are the recommended way to represent orbits.

The instance EquinoctialOrbit is guaranteed to be immutable.

Author:

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

See Also:

Orbit, KeplerianOrbit, CircularOrbit, CartesianOrbit, Serialized Form

Constructor Summary

Constructors

Constructor	Description
EquinoctialOrbit(double a, double ex, double ey, double hx, double hy, double l, double aDot, double exDot, double eyDot, double hxDot, double hyDot, double lDot, PositionAngle type, Frame frame, AbsoluteDate date, double mu)	Creates a new instance.
EquinoctialOrbit(double a, double ex, double ey, double hx, double hy, double l, PositionAngle type, Frame frame, AbsoluteDate date, double mu)	Creates a new instance.
EquinoctialOrbit(Orbit op)	Constructor from any kind of orbital parameters.
EquinoctialOrbit(PVCoordinates pvCoordinates, Frame frame, AbsoluteDate date, double mu)	Constructor from Cartesian parameters.
EquinoctialOrbit(TimeStampedPVCoordinates pvCoordinates, Frame frame, double mu)	Constructor from Cartesian parameters.

Method Summary

Modifier and Type	Method	Description
void	addKeplerContribution(PositionAngle type, double gm, double[] pDot)	Add the contribution of the Keplerian motion to parameters derivatives
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.
static double	eccentricToMean(double lE, double ex, double ey)	Computes the mean longitude argument from the eccentric longitude argument.
static double	eccentricToTrue(double lE, double ex, double ey)	Computes the true longitude argument from the eccentric longitude argument.
double	getA()	Get the semi-major axis.
double	getADot()	Get the semi-major axis derivative.
double	getE()	Get the eccentricity.
double	getEDot()	Get the eccentricity derivative.
double	getEquinoctialEx()	Get the first component of the equinoctial eccentricity vector derivative.
double	getEquinoctialExDot()	Get the first component of the equinoctial eccentricity vector.
double	getEquinoctialEy()	Get the second component of the equinoctial eccentricity vector derivative.
double	getEquinoctialEyDot()	Get the second component of the equinoctial eccentricity vector.
double	getHx()	Get the first component of the inclination vector.
double	getHxDot()	Get the first component of the inclination vector derivative.
double	getHy()	Get the second component of the inclination vector.
double	getHyDot()	Get the second component of the inclination vector derivative.
double	getI()	Get the inclination.
double	getIDot()	Get the inclination derivative.
double	getL(PositionAngle type)	Get the longitude argument.
double	getLDot(PositionAngle type)	Get the longitude argument derivative.
double	getLE()	Get the eccentric longitude argument.
double	getLEDot()	Get the eccentric longitude argument derivative.
double	getLM()	Get the mean longitude argument.
double	getLMDot()	Get the mean longitude argument derivative.
double	getLv()	Get the true longitude argument.
double	getLvDot()	Get the true longitude argument derivative.
OrbitType	getType()	Get the orbit type.
protected TimeStampedPVCoordinates	initPVCoordinates()	Compute the position/velocity coordinates from the canonical parameters.
EquinoctialOrbit	interpolate(AbsoluteDate date, Stream<Orbit> sample)	Get an interpolated instance.
static double	meanToEccentric(double lM, double ex, double ey)	Computes the eccentric longitude argument from the mean longitude argument.
EquinoctialOrbit	shiftedBy(double dt)	Get a time-shifted orbit.
String	toString()	Returns a string representation of this equinoctial parameters object.
static double	trueToEccentric(double lv, double ex, double ey)	Computes the eccentric longitude argument from the true longitude argument.

Methods inherited from class java.lang.Object

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

Methods inherited from class org.orekit.orbits.Orbit

fillHalfRow, fillHalfRow, fillHalfRow, fillHalfRow, fillHalfRow, fillHalfRow, getDate, getFrame, getJacobianWrtCartesian, getJacobianWrtParameters, getKeplerianMeanMotion, getKeplerianPeriod, getMu, getPVCoordinates, getPVCoordinates, getPVCoordinates, hasDerivatives, hasNonKeplerianAcceleration

Methods inherited from interface org.orekit.time.TimeInterpolable

interpolate

Constructor Detail

EquinoctialOrbit

public EquinoctialOrbit(double a,
                        double ex,
                        double ey,
                        double hx,
                        double hy,
                        double l,
                        PositionAngle type,
                        Frame frame,
                        AbsoluteDate date,
                        double mu)
                 throws IllegalArgumentException

Creates a new instance.

Parameters:

a - semi-major axis (m)

ex - e cos(ω + Ω), first component of eccentricity vector

ey - e sin(ω + Ω), second component of eccentricity vector

hx - tan(i/2) cos(Ω), first component of inclination vector

hy - tan(i/2) sin(Ω), second component of inclination vector

l - (M or E or v) + ω + Ω, mean, eccentric or true longitude argument (rad)

type - type of longitude argument

frame - the frame in which the parameters are defined (must be a pseudo-inertial frame)

date - date of the orbital parameters

mu - central attraction coefficient (m³/s²)

Throws:

IllegalArgumentException - if eccentricity is equal to 1 or larger or if frame is not a pseudo-inertial frame

EquinoctialOrbit

public EquinoctialOrbit(double a,
                        double ex,
                        double ey,
                        double hx,
                        double hy,
                        double l,
                        double aDot,
                        double exDot,
                        double eyDot,
                        double hxDot,
                        double hyDot,
                        double lDot,
                        PositionAngle type,
                        Frame frame,
                        AbsoluteDate date,
                        double mu)
                 throws IllegalArgumentException

Creates a new instance.

Parameters:

a - semi-major axis (m)

ex - e cos(ω + Ω), first component of eccentricity vector

ey - e sin(ω + Ω), second component of eccentricity vector

hx - tan(i/2) cos(Ω), first component of inclination vector

hy - tan(i/2) sin(Ω), second component of inclination vector

l - (M or E or v) + ω + Ω, mean, eccentric or true longitude argument (rad)

aDot - semi-major axis derivative (m/s)

exDot - d(e cos(ω + Ω))/dt, first component of eccentricity vector derivative

eyDot - d(e sin(ω + Ω))/dt, second component of eccentricity vector derivative

hxDot - d(tan(i/2) cos(Ω))/dt, first component of inclination vector derivative

hyDot - d(tan(i/2) sin(Ω))/dt, second component of inclination vector derivative

lDot - d(M or E or v) + ω + Ω)/dr, mean, eccentric or true longitude argument derivative (rad/s)

type - type of longitude argument

frame - the frame in which the parameters are defined (must be a pseudo-inertial frame)

date - date of the orbital parameters

mu - central attraction coefficient (m³/s²)

Throws:

IllegalArgumentException - if eccentricity is equal to 1 or larger or if frame is not a pseudo-inertial frame

EquinoctialOrbit

public EquinoctialOrbit(TimeStampedPVCoordinates pvCoordinates,
                        Frame frame,
                        double mu)
                 throws IllegalArgumentException

Constructor from Cartesian parameters.

The acceleration provided in pvCoordinates is accessible using Orbit.getPVCoordinates() and Orbit.getPVCoordinates(Frame). All other methods use mu and the position to compute the acceleration, including shiftedBy(double) and Orbit.getPVCoordinates(AbsoluteDate, Frame).

Parameters:

pvCoordinates - the position, velocity and acceleration

frame - the frame in which are defined the PVCoordinates (must be a pseudo-inertial frame)

mu - central attraction coefficient (m³/s²)

Throws:

IllegalArgumentException - if eccentricity is equal to 1 or larger or if frame is not a pseudo-inertial frame

EquinoctialOrbit

public EquinoctialOrbit(PVCoordinates pvCoordinates,
                        Frame frame,
                        AbsoluteDate date,
                        double mu)
                 throws IllegalArgumentException

Constructor from Cartesian parameters.

The acceleration provided in pvCoordinates is accessible using Orbit.getPVCoordinates() and Orbit.getPVCoordinates(Frame). All other methods use mu and the position to compute the acceleration, including shiftedBy(double) and Orbit.getPVCoordinates(AbsoluteDate, Frame).

Parameters:

pvCoordinates - the position end velocity

frame - the frame in which are defined the PVCoordinates (must be a pseudo-inertial frame)

date - date of the orbital parameters

mu - central attraction coefficient (m³/s²)

Throws:

IllegalArgumentException - if eccentricity is equal to 1 or larger or if frame is not a pseudo-inertial frame

EquinoctialOrbit

public EquinoctialOrbit(Orbit op)

Constructor from any kind of orbital parameters.

Parameters:

op - orbital parameters to copy

Method Detail

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)

getADot

public double getADot()

Get the semi-major axis derivative.

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

If the orbit was created without derivatives, the value returned is Double.NaN.

Specified by:

getADot in class Orbit

Returns:

semi-major axis derivative (m/s)

See Also:

Orbit.hasDerivatives()

getEquinoctialEx

public double getEquinoctialEx()

Get the first component of the equinoctial eccentricity vector derivative.

Specified by:

getEquinoctialEx in class Orbit

Returns:

first component of the equinoctial eccentricity vector derivative

getEquinoctialExDot

public double getEquinoctialExDot()

Get the first component of the equinoctial eccentricity vector.

If the orbit was created without derivatives, the value returned is Double.NaN.

Specified by:

getEquinoctialExDot in class Orbit

Returns:

first component of the equinoctial eccentricity vector

See Also:

Orbit.hasDerivatives()

getEquinoctialEy

public double getEquinoctialEy()

Get the second component of the equinoctial eccentricity vector derivative.

Specified by:

getEquinoctialEy in class Orbit

Returns:

second component of the equinoctial eccentricity vector derivative

getEquinoctialEyDot

public double getEquinoctialEyDot()

Get the second component of the equinoctial eccentricity vector.

If the orbit was created without derivatives, the value returned is Double.NaN.

Specified by:

getEquinoctialEyDot in class Orbit

Returns:

second component of the equinoctial eccentricity vector

See Also:

Orbit.hasDerivatives()

getHx

public double getHx()

Get the first component of the inclination vector.

Specified by:

getHx in class Orbit

Returns:

first component of the inclination vector

getHxDot

public double getHxDot()

Get the first component of the inclination vector derivative.

If the orbit was created without derivatives, the value returned is Double.NaN.

Specified by:

getHxDot in class Orbit

Returns:

first component of the inclination vector derivative

See Also:

Orbit.hasDerivatives()

getHy

public double getHy()

Get the second component of the inclination vector.

Specified by:

getHy in class Orbit

Returns:

second component of the inclination vector

getHyDot

public double getHyDot()

Get the second component of the inclination vector derivative.

If the orbit was created without derivatives, the value returned is Double.NaN.

Specified by:

getHyDot in class Orbit

Returns:

second component of the inclination vector derivative

See Also:

Orbit.hasDerivatives()

getLv

public double getLv()

Get the true longitude argument.

Specified by:

getLv in class Orbit

Returns:

v + ω + Ω true longitude argument (rad)

getLvDot

public double getLvDot()

Get the true longitude argument derivative.

If the orbit was created without derivatives, the value returned is Double.NaN.

Specified by:

getLvDot in class Orbit

Returns:

d(v + ω + Ω)/dt true longitude argument derivative (rad/s)

See Also:

Orbit.hasDerivatives()

getLE

public double getLE()

Get the eccentric longitude argument.

Specified by:

getLE in class Orbit

Returns:

E + ω + Ω eccentric longitude argument (rad)

getLEDot

public double getLEDot()

Get the eccentric longitude argument derivative.

If the orbit was created without derivatives, the value returned is Double.NaN.

Specified by:

getLEDot in class Orbit

Returns:

d(E + ω + Ω)/dt eccentric longitude argument derivative (rad/s)

See Also:

Orbit.hasDerivatives()

getLM

public double getLM()

Get the mean longitude argument.

Specified by:

getLM in class Orbit

Returns:

M + ω + Ω mean longitude argument (rad)

getLMDot

public double getLMDot()

Get the mean longitude argument derivative.

If the orbit was created without derivatives, the value returned is Double.NaN.

Specified by:

getLMDot in class Orbit

Returns:

d(M + ω + Ω)/dt mean longitude argument derivative (rad/s)

See Also:

Orbit.hasDerivatives()

getL

public double getL(PositionAngle type)

Get the longitude argument.

Parameters:

type - type of the angle

Returns:

longitude argument (rad)

getLDot

public double getLDot(PositionAngle type)

Get the longitude argument derivative.

Parameters:

type - type of the angle

Returns:

longitude argument derivative (rad/s)

eccentricToTrue

public static double eccentricToTrue(double lE,
                                     double ex,
                                     double ey)

Computes the true longitude argument from the eccentric longitude argument.

Parameters:

lE - = E + ω + Ω eccentric longitude argument (rad)

ex - first component of the eccentricity vector

ey - second component of the eccentricity vector

Returns:

the true longitude argument

trueToEccentric

public static double trueToEccentric(double lv,
                                     double ex,
                                     double ey)

Computes the eccentric longitude argument from the true longitude argument.

Parameters:

lv - = v + ω + Ω true longitude argument (rad)

ex - first component of the eccentricity vector

ey - second component of the eccentricity vector

Returns:

the eccentric longitude argument

meanToEccentric

public static double meanToEccentric(double lM,
                                     double ex,
                                     double ey)

Computes the eccentric longitude argument from the mean longitude argument.

Parameters:

lM - = M + ω + Ω mean longitude argument (rad)

ex - first component of the eccentricity vector

ey - second component of the eccentricity vector

Returns:

the eccentric longitude argument

eccentricToMean

public static double eccentricToMean(double lE,
                                     double ex,
                                     double ey)

Computes the mean longitude argument from the eccentric longitude argument.

Parameters:

lE - = E + ω + Ω mean longitude argument (rad)

ex - first component of the eccentricity vector

ey - second component of the eccentricity vector

Returns:

the mean longitude argument

getE

public double getE()

Get the eccentricity.

Specified by:

getE in class Orbit

Returns:

eccentricity

getEDot

public double getEDot()

Get the eccentricity derivative.

If the orbit was created without derivatives, the value returned is Double.NaN.

Specified by:

getEDot in class Orbit

Returns:

eccentricity derivative

See Also:

Orbit.hasDerivatives()

getI

public double getI()

Get the inclination.

Specified by:

getI in class Orbit

Returns:

inclination (rad)

getIDot

public double getIDot()

Get the inclination derivative.

If the orbit was created without derivatives, the value returned is Double.NaN.

Specified by:

getIDot in class Orbit

Returns:

inclination derivative (rad/s)

See Also:

Orbit.hasDerivatives()

initPVCoordinates

protected TimeStampedPVCoordinates initPVCoordinates()

Compute the position/velocity coordinates from the canonical parameters.

Specified by:

initPVCoordinates in class Orbit

Returns:

computed position/velocity coordinates

shiftedBy

public EquinoctialOrbit shiftedBy(double dt)

Get a time-shifted orbit.

The orbit can be slightly shifted to close dates. The shifting model is a Keplerian one if no derivatives are available in the orbit, or Keplerian plus quadratic effect of the non-Keplerian acceleration if derivatives are available. Shifting is not intended as a replacement for proper orbit propagation but should be sufficient for small time shifts or coarse accuracy.

Specified by:

shiftedBy in interface TimeShiftable<Orbit>

Specified by:

shiftedBy in class Orbit

Parameters:

dt - time shift in seconds

Returns:

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

interpolate

public EquinoctialOrbit interpolate(AbsoluteDate date,
                                    Stream<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.

Note that this method is designed for small samples only (say up to about 10-20 points) so it can be implemented using polynomial interpolation (typically Hermite interpolation). Using too much points may induce Runge's phenomenon and numerical problems (including NaN appearing).

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

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

If orbit interpolation on large samples is needed, using the Ephemeris class is a better way than using this low-level interpolation. The Ephemeris class automatically handles selection of a neighboring sub-sample with a predefined number of point from a large global sample in a thread-safe way.

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()

addKeplerContribution

public void addKeplerContribution(PositionAngle type,
                                  double gm,
                                  double[] pDot)

Add the contribution of the Keplerian motion to parameters derivatives

This method is used by integration-based propagators to evaluate the part of Keplerian motion to evolution of the orbital state.

Specified by:

addKeplerContribution 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()

Returns a string representation of this equinoctial parameters object.

Overrides:

toString in class Object

Returns:

a string representation of this object