Package org.orekit.orbits

Class FieldCircularOrbit<T extends org.hipparchus.RealFieldElement<T>>

java.lang.Object

org.orekit.orbits.FieldOrbit<T>

org.orekit.orbits.FieldCircularOrbit<T>

All Implemented Interfaces:

FieldTimeInterpolable<FieldOrbit<T>,T>, FieldTimeShiftable<FieldOrbit<T>,T>, FieldTimeStamped<T>, FieldPVCoordinatesProvider<T>

public class FieldCircularOrbit<T extends org.hipparchus.RealFieldElement<T>>
extends FieldOrbit<T>

This class handles circular orbital parameters.

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

• a
• e_x = e cos(ω)
• e_y = e sin(ω)
• i
• Ω
• α_v = v + ω

where Ω stands for the Right Ascension of the Ascending Node and α_v stands for the true latitude argument

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 circular (but not equatorial), the circular parameters are still unambiguously defined whereas some Keplerian elements (more precisely ω and Ω) become ambiguous. When orbit is equatorial, neither the Keplerian nor the circular parameters can be defined unambiguously. equinoctial orbits is the recommended way to represent orbits.

The instance CircularOrbit is guaranteed to be immutable.

Since:

9.0

Author:

Luc Maisonobe, Fabien Maussion, Véronique Pommier-Maurussane

See Also:

Orbit, KeplerianOrbit, CartesianOrbit, EquinoctialOrbit

Constructor Summary

Constructors

Constructor	Description
FieldCircularOrbit(FieldOrbit<T> op)	Constructor from any kind of orbital parameters.
FieldCircularOrbit(FieldPVCoordinates<T> PVCoordinates, Frame frame, FieldAbsoluteDate<T> date, double mu)	Constructor from Cartesian parameters.
FieldCircularOrbit(TimeStampedFieldPVCoordinates<T> pvCoordinates, Frame frame, double mu)	Constructor from Cartesian parameters.
FieldCircularOrbit(T a, T ex, T ey, T i, T raan, T alpha, PositionAngle type, Frame frame, FieldAbsoluteDate<T> date, double mu)	Creates a new instance.
FieldCircularOrbit(T a, T ex, T ey, T i, T raan, T alpha, T aDot, T exDot, T eyDot, T iDot, T raanDot, T alphaDot, PositionAngle type, Frame frame, FieldAbsoluteDate<T> date, double mu)	Creates a new instance.

Method Summary

Modifier and Type	Method	Description
void	addKeplerContribution(PositionAngle type, double gm, T[] pDot)	Add the contribution of the Keplerian motion to parameters derivatives
static <T extends org.hipparchus.RealFieldElement<T>> org.hipparchus.geometry.euclidean.threed.FieldVector3D<T>	circularToPosition(T a, T ex, T ey, T i, T raan, T alphaV, double mu)	Deprecated. as of 9.3, replaced by FieldCircularOrbit(RealFieldElement, RealFieldElement, RealFieldElement, RealFieldElement, RealFieldElement, RealFieldElement, PositionAngle, Frame, FieldAbsoluteDate, double) and FieldOrbit.getPVCoordinates()
protected T[][]	computeJacobianEccentricWrtCartesian()	Compute the Jacobian of the orbital parameters with eccentric angle with respect to the Cartesian parameters.
protected T[][]	computeJacobianMeanWrtCartesian()	Compute the Jacobian of the orbital parameters with mean angle with respect to the Cartesian parameters.
protected T[][]	computeJacobianTrueWrtCartesian()	Compute the Jacobian of the orbital parameters with true angle with respect to the Cartesian parameters.
static <T extends org.hipparchus.RealFieldElement<T>> T	eccentricToMean(T alphaE, T ex, T ey)	Computes the mean latitude argument from the eccentric latitude argument.
static <T extends org.hipparchus.RealFieldElement<T>> T	eccentricToTrue(T alphaE, T ex, T ey)	Computes the true latitude argument from the eccentric latitude argument.
T	getA()	Get the semi-major axis.
T	getADot()	Get the semi-major axis derivative.
T	getAlpha(PositionAngle type)	Get the latitude argument.
T	getAlphaDot(PositionAngle type)	Get the latitude argument derivative.
T	getAlphaE()	Get the eccentric latitude argument.
T	getAlphaEDot()	Get the eccentric latitude argument derivative.
T	getAlphaM()	Get the mean latitude argument.
T	getAlphaMDot()	Get the mean latitude argument derivative.
T	getAlphaV()	Get the true latitude argument.
T	getAlphaVDot()	Get the true latitude argument derivative.
T	getCircularEx()	Get the first component of the circular eccentricity vector.
T	getCircularExDot()	Get the first component of the circular eccentricity vector derivative.
T	getCircularEy()	Get the second component of the circular eccentricity vector.
T	getCircularEyDot()	Get the second component of the circular eccentricity vector derivative.
T	getE()	Get the eccentricity.
T	getEDot()	Get the eccentricity derivative.
T	getEquinoctialEx()	Get the first component of the equinoctial eccentricity vector.
T	getEquinoctialExDot()	Get the first component of the equinoctial eccentricity vector.
T	getEquinoctialEy()	Get the second component of the equinoctial eccentricity vector.
T	getEquinoctialEyDot()	Get the second component of the equinoctial eccentricity vector.
T	getHx()	Get the first component of the inclination vector.
T	getHxDot()	Get the first component of the inclination vector derivative.
T	getHy()	Get the second component of the inclination vector.
T	getHyDot()	Get the second component of the inclination vector derivative.
T	getI()	Get the inclination.
T	getIDot()	Get the inclination derivative.
T	getLE()	Get the eccentric longitude argument.
T	getLEDot()	Get the eccentric longitude argument derivative.
T	getLM()	Get the mean longitude argument.
T	getLMDot()	Get the mean longitude argument derivative.
T	getLv()	Get the true longitude argument.
T	getLvDot()	Get the true longitude argument derivative.
T	getRightAscensionOfAscendingNode()	Get the right ascension of the ascending node.
T	getRightAscensionOfAscendingNodeDot()	Get the right ascension of the ascending node derivative.
OrbitType	getType()	Get the orbit type.
boolean	hasDerivatives()	Check if orbit includes derivatives.
protected TimeStampedFieldPVCoordinates<T>	initPVCoordinates()	Compute the position/velocity coordinates from the canonical parameters.
FieldCircularOrbit<T>	interpolate(FieldAbsoluteDate<T> date, Stream<FieldOrbit<T>> sample)	Get an interpolated instance.
static <T extends org.hipparchus.RealFieldElement<T>> T	meanToEccentric(T alphaM, T ex, T ey)	Computes the eccentric latitude argument from the mean latitude argument.
static <T extends org.hipparchus.RealFieldElement<T>> T	normalizeAngle(T a, T center)	Normalize an angle in a 2π wide interval around a center value.
FieldCircularOrbit<T>	shiftedBy(double dt)	Get a time-shifted instance.
FieldCircularOrbit<T>	shiftedBy(T dt)	Get a time-shifted orbit.
CircularOrbit	toOrbit()	Transforms the FieldOrbit instance into an Orbit instance.
String	toString()	Returns a string representation of this Orbit object.
static <T extends org.hipparchus.RealFieldElement<T>> T	trueToEccentric(T alphaV, T ex, T ey)	Computes the eccentric latitude argument from the true latitude argument.

Methods inherited from class org.orekit.orbits.FieldOrbit

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

Methods inherited from interface org.orekit.time.FieldTimeInterpolable

interpolate

Methods inherited from class java.lang.Object

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

Constructor Detail

FieldCircularOrbit

public FieldCircularOrbit(T a,
                          T ex,
                          T ey,
                          T i,
                          T raan,
                          T alpha,
                          PositionAngle type,
                          Frame frame,
                          FieldAbsoluteDate<T> date,
                          double mu)
                   throws IllegalArgumentException

Creates a new instance.

Parameters:

a - semi-major axis (m)

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

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

i - inclination (rad)

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

alpha - an + ω, mean, eccentric or true latitude argument (rad)

type - type of latitude argument

frame - the frame in which are defined the parameters (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

FieldCircularOrbit

public FieldCircularOrbit(T a,
                          T ex,
                          T ey,
                          T i,
                          T raan,
                          T alpha,
                          T aDot,
                          T exDot,
                          T eyDot,
                          T iDot,
                          T raanDot,
                          T alphaDot,
                          PositionAngle type,
                          Frame frame,
                          FieldAbsoluteDate<T> date,
                          double mu)
                   throws IllegalArgumentException

Creates a new instance.

Parameters:

a - semi-major axis (m)

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

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

i - inclination (rad)

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

alpha - an + ω, mean, eccentric or true latitude argument (rad)

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

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

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

iDot - inclination derivative(rad/s)

raanDot - right ascension of ascending node derivative (rad/s)

alphaDot - d(an + ω), mean, eccentric or true latitude argument derivative (rad/s)

type - type of latitude argument

frame - the frame in which are defined the parameters (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

FieldCircularOrbit

public FieldCircularOrbit(TimeStampedFieldPVCoordinates<T> pvCoordinates,
                          Frame frame,
                          double mu)
                   throws IllegalArgumentException

Constructor from Cartesian parameters.

The acceleration provided in FieldPVCoordinates is accessible using FieldOrbit.getPVCoordinates() and FieldOrbit.getPVCoordinates(Frame). All other methods use mu and the position to compute the acceleration, including shiftedBy(RealFieldElement) and FieldOrbit.getPVCoordinates(FieldAbsoluteDate, Frame).

Parameters:

pvCoordinates - the FieldPVCoordinates in inertial frame

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

mu - central attraction coefficient (m³/s²)

Throws:

IllegalArgumentException - if frame is not a pseudo-inertial frame

FieldCircularOrbit

public FieldCircularOrbit(FieldPVCoordinates<T> PVCoordinates,
                          Frame frame,
                          FieldAbsoluteDate<T> date,
                          double mu)
                   throws IllegalArgumentException

Constructor from Cartesian parameters.

The acceleration provided in FieldPVCoordinates is accessible using FieldOrbit.getPVCoordinates() and FieldOrbit.getPVCoordinates(Frame). All other methods use mu and the position to compute the acceleration, including shiftedBy(RealFieldElement) and FieldOrbit.getPVCoordinates(FieldAbsoluteDate, Frame).

Parameters:

PVCoordinates - the FieldPVCoordinates in inertial frame

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

date - date of the orbital parameters

mu - central attraction coefficient (m³/s²)

Throws:

IllegalArgumentException - if frame is not a pseudo-inertial frame

FieldCircularOrbit

public FieldCircularOrbit(FieldOrbit<T> 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 FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

orbit type

getA

public T getA()

Get the semi-major axis.

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

Specified by:

getA in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

semi-major axis (m)

getADot

public T 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 null.

Specified by:

getADot in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

semi-major axis derivative (m/s)

getEquinoctialEx

public T getEquinoctialEx()

Get the first component of the equinoctial eccentricity vector.

Specified by:

getEquinoctialEx in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

first component of the equinoctial eccentricity vector

getEquinoctialExDot

public T getEquinoctialExDot()

Get the first component of the equinoctial eccentricity vector.

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

Specified by:

getEquinoctialExDot in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

first component of the equinoctial eccentricity vector

getEquinoctialEy

public T getEquinoctialEy()

Get the second component of the equinoctial eccentricity vector.

Specified by:

getEquinoctialEy in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

second component of the equinoctial eccentricity vector

getEquinoctialEyDot

public T getEquinoctialEyDot()

Get the second component of the equinoctial eccentricity vector.

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

Specified by:

getEquinoctialEyDot in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

second component of the equinoctial eccentricity vector

getCircularEx

public T getCircularEx()

Get the first component of the circular eccentricity vector.

Returns:

ex = e cos(ω), first component of the circular eccentricity vector

getCircularExDot

public T getCircularExDot()

Get the first component of the circular eccentricity vector derivative.

Returns:

d(ex)/dt = d(e cos(ω))/dt, first component of the circular eccentricity vector derivative

getCircularEy

public T getCircularEy()

Get the second component of the circular eccentricity vector.

Returns:

ey = e sin(ω), second component of the circular eccentricity vector

getCircularEyDot

public T getCircularEyDot()

Get the second component of the circular eccentricity vector derivative.

Returns:

d(ey)/dt = d(e sin(ω))/dt, second component of the circular eccentricity vector derivative

getHx

public T getHx()

Get the first component of the inclination vector.

Specified by:

getHx in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

first component of the inclination vector

getHxDot

public T getHxDot()

Get the first component of the inclination vector derivative.

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

Specified by:

getHxDot in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

first component of the inclination vector derivative

getHy

public T getHy()

Get the second component of the inclination vector.

Specified by:

getHy in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

second component of the inclination vector

getHyDot

public T getHyDot()

Get the second component of the inclination vector derivative.

Specified by:

getHyDot in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

second component of the inclination vector derivative

getAlphaV

public T getAlphaV()

Get the true latitude argument.

Returns:

v + ω true latitude argument (rad)

getAlphaVDot

public T getAlphaVDot()

Get the true latitude argument derivative.

Returns:

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

getAlphaE

public T getAlphaE()

Get the eccentric latitude argument.

Returns:

E + ω eccentric latitude argument (rad)

getAlphaEDot

public T getAlphaEDot()

Get the eccentric latitude argument derivative.

Returns:

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

getAlphaM

public T getAlphaM()

Get the mean latitude argument.

Returns:

M + ω mean latitude argument (rad)

getAlphaMDot

public T getAlphaMDot()

Get the mean latitude argument derivative.

Returns:

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

getAlpha

public T getAlpha(PositionAngle type)

Get the latitude argument.

Parameters:

type - type of the angle

Returns:

latitude argument (rad)

getAlphaDot

public T getAlphaDot(PositionAngle type)

Get the latitude argument derivative.

Parameters:

type - type of the angle

Returns:

latitude argument derivative (rad/s)

eccentricToTrue

public static <T extends org.hipparchus.RealFieldElement<T>> T eccentricToTrue(T alphaE,
                                                                               T ex,
                                                                               T ey)

Computes the true latitude argument from the eccentric latitude argument.

Type Parameters:

T - Type of the field elements

Parameters:

alphaE - = E + ω eccentric latitude argument (rad)

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

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

Returns:

the true latitude argument.

trueToEccentric

public static <T extends org.hipparchus.RealFieldElement<T>> T trueToEccentric(T alphaV,
                                                                               T ex,
                                                                               T ey)

Computes the eccentric latitude argument from the true latitude argument.

Type Parameters:

T - Type of the field elements

Parameters:

alphaV - = v + ω true latitude argument (rad)

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

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

Returns:

the eccentric latitude argument.

meanToEccentric

public static <T extends org.hipparchus.RealFieldElement<T>> T meanToEccentric(T alphaM,
                                                                               T ex,
                                                                               T ey)

Computes the eccentric latitude argument from the mean latitude argument.

Type Parameters:

T - Type of the field elements

Parameters:

alphaM - = M + ω mean latitude argument (rad)

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

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

Returns:

the eccentric latitude argument.

eccentricToMean

public static <T extends org.hipparchus.RealFieldElement<T>> T eccentricToMean(T alphaE,
                                                                               T ex,
                                                                               T ey)

Computes the mean latitude argument from the eccentric latitude argument.

Type Parameters:

T - Type of the field elements

Parameters:

alphaE - = E + ω eccentric latitude argument (rad)

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

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

Returns:

the mean latitude argument.

circularToPosition

@Deprecated
public static <T extends org.hipparchus.RealFieldElement<T>> org.hipparchus.geometry.euclidean.threed.FieldVector3D<T> circularToPosition(T a,
                                                                                                                                          T ex,
                                                                                                                                          T ey,
                                                                                                                                          T i,
                                                                                                                                          T raan,
                                                                                                                                          T alphaV,
                                                                                                                                          double mu)

Deprecated. as of 9.3, replaced by FieldCircularOrbit(RealFieldElement, RealFieldElement, RealFieldElement, RealFieldElement, RealFieldElement, RealFieldElement, PositionAngle, Frame, FieldAbsoluteDate, double) and FieldOrbit.getPVCoordinates()

Compute position from circular parameters.

Type Parameters:

T - type of the fiels elements

Parameters:

a - semi-major axis (m)

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

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

i - inclination (rad)

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

alphaV - v + ω true latitude argument (rad)

mu - central attraction coefficient (m³/s²)

Returns:

position vector

getE

public T getE()

Get the eccentricity.

Specified by:

getE in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

eccentricity

getEDot

public T getEDot()

Get the eccentricity derivative.

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

Specified by:

getEDot in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

eccentricity derivative

getI

public T getI()

Get the inclination.

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

Specified by:

getI in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

inclination (rad)

getIDot

public T getIDot()

Get the inclination derivative.

Specified by:

getIDot in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

inclination derivative (rad/s)

getRightAscensionOfAscendingNode

public T getRightAscensionOfAscendingNode()

Get the right ascension of the ascending node.

Returns:

right ascension of the ascending node (rad)

getRightAscensionOfAscendingNodeDot

public T getRightAscensionOfAscendingNodeDot()

Get the right ascension of the ascending node derivative.

Returns:

right ascension of the ascending node derivative (rad/s)

getLv

public T getLv()

Get the true longitude argument.

Specified by:

getLv in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

v + ω + Ω true longitude argument (rad)

getLvDot

public T getLvDot()

Get the true longitude argument derivative.

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

Specified by:

getLvDot in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

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

getLE

public T getLE()

Get the eccentric longitude argument.

Specified by:

getLE in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

E + ω + Ω eccentric longitude argument (rad)

getLEDot

public T getLEDot()

Get the eccentric longitude argument derivative.

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

Specified by:

getLEDot in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

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

getLM

public T getLM()

Get the mean longitude argument.

Specified by:

getLM in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

M + ω + Ω mean longitude argument (rad)

getLMDot

public T getLMDot()

Get the mean longitude argument derivative.

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

Specified by:

getLMDot in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

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

hasDerivatives

public boolean hasDerivatives()

Check if orbit includes derivatives.

Specified by:

hasDerivatives in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

true if orbit includes derivatives

See Also:

FieldOrbit.getADot(), FieldOrbit.getEquinoctialExDot(), FieldOrbit.getEquinoctialEyDot(), FieldOrbit.getHxDot(), FieldOrbit.getHyDot(), FieldOrbit.getLEDot(), FieldOrbit.getLvDot(), FieldOrbit.getLMDot(), FieldOrbit.getEDot(), FieldOrbit.getIDot()

initPVCoordinates

protected TimeStampedFieldPVCoordinates<T> initPVCoordinates()

Compute the position/velocity coordinates from the canonical parameters.

Specified by:

initPVCoordinates in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

computed position/velocity coordinates

shiftedBy

public FieldCircularOrbit<T> shiftedBy(double dt)

Get a time-shifted instance.

Parameters:

dt - time shift in seconds

Returns:

a new instance, shifted with respect to instance (which is not changed)

shiftedBy

public FieldCircularOrbit<T> shiftedBy(T 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:

shiftedBy in interface FieldTimeShiftable<FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>,T extends org.hipparchus.RealFieldElement<T>>

Specified by:

shiftedBy in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Parameters:

dt - time shift in seconds

Returns:

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

interpolate

public FieldCircularOrbit<T> interpolate(FieldAbsoluteDate<T> date,
                                         Stream<FieldOrbit<T>> 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 circular 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 T[][] 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 FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

6x6 Jacobian matrix

See Also:

FieldOrbit.computeJacobianEccentricWrtCartesian(), FieldOrbit.computeJacobianTrueWrtCartesian()

computeJacobianEccentricWrtCartesian

protected T[][] 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 FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

6x6 Jacobian matrix

See Also:

FieldOrbit.computeJacobianMeanWrtCartesian(), FieldOrbit.computeJacobianTrueWrtCartesian()

computeJacobianTrueWrtCartesian

protected T[][] 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 FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

6x6 Jacobian matrix

See Also:

FieldOrbit.computeJacobianMeanWrtCartesian(), FieldOrbit.computeJacobianEccentricWrtCartesian()

addKeplerContribution

public void addKeplerContribution(PositionAngle type,
                                  double gm,
                                  T[] 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 FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

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 Orbit object.

Overrides:

toString in class Object

Returns:

a string representation of this object

normalizeAngle

public static <T extends org.hipparchus.RealFieldElement<T>> T normalizeAngle(T a,
                                                                              T center)

Normalize an angle in a 2π wide interval around a center value.

This method has three main uses:

• normalize an angle between 0 and 2π:
  a = MathUtils.normalizeAngle(a, FastMath.PI);
• normalize an angle between -π and +π
  a = MathUtils.normalizeAngle(a, 0.0);
• compute the angle between two defining angular positions:
  angle = MathUtils.normalizeAngle(end, start) - start;

Note that due to numerical accuracy and since π cannot be represented exactly, the result interval is closed, it cannot be half-closed as would be more satisfactory in a purely mathematical view.

Type Parameters:

T - the type of the field elements

Parameters:

a - angle to normalize

center - center of the desired 2π interval for the result

Returns:

a-2kπ with integer k and center-π <= a-2kπ <= center+π

toOrbit

public CircularOrbit toOrbit()

Description copied from class: FieldOrbit

Transforms the FieldOrbit instance into an Orbit instance.

Specified by:

toOrbit in class FieldOrbit<T extends org.hipparchus.RealFieldElement<T>>

Returns:

Orbit instance with same properties