public class FieldEquinoctialOrbit<T extends CalculusFieldElement<T>> extends FieldOrbit<T>
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 + Ωwhere 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.
Orbit
,
KeplerianOrbit
,
CircularOrbit
,
CartesianOrbit
Constructor and Description |
---|
FieldEquinoctialOrbit(FieldOrbit<T> op)
Constructor from any kind of orbital parameters.
|
FieldEquinoctialOrbit(FieldPVCoordinates<T> pvCoordinates,
Frame frame,
FieldAbsoluteDate<T> date,
T mu)
Constructor from Cartesian parameters.
|
FieldEquinoctialOrbit(TimeStampedFieldPVCoordinates<T> pvCoordinates,
Frame frame,
T mu)
Constructor from Cartesian parameters.
|
FieldEquinoctialOrbit(T a,
T ex,
T ey,
T hx,
T hy,
T l,
PositionAngle type,
Frame frame,
FieldAbsoluteDate<T> date,
T mu)
Creates a new instance.
|
FieldEquinoctialOrbit(T a,
T ex,
T ey,
T hx,
T hy,
T l,
T aDot,
T exDot,
T eyDot,
T hxDot,
T hyDot,
T lDot,
PositionAngle type,
Frame frame,
FieldAbsoluteDate<T> date,
T mu)
Creates a new instance.
|
Modifier and Type | Method and Description |
---|---|
void |
addKeplerContribution(PositionAngle type,
T gm,
T[] pDot)
Add the contribution of the Keplerian motion to parameters derivatives
|
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 CalculusFieldElement<T>> |
eccentricToMean(T lE,
T ex,
T ey)
Computes the mean longitude argument from the eccentric longitude argument.
|
static <T extends CalculusFieldElement<T>> |
eccentricToTrue(T lE,
T ex,
T ey)
Computes the true longitude argument from the eccentric longitude argument.
|
T |
getA()
Get the semi-major axis.
|
T |
getADot()
Get the semi-major axis 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 |
getL(PositionAngle type)
Get the longitude argument.
|
T |
getLDot(PositionAngle type)
Get the longitude argument 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.
|
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.
|
FieldEquinoctialOrbit<T> |
interpolate(FieldAbsoluteDate<T> date,
Stream<FieldOrbit<T>> sample)
Get an interpolated instance.
|
static <T extends CalculusFieldElement<T>> |
meanToEccentric(T lM,
T ex,
T ey)
Computes the eccentric longitude argument from the mean longitude argument.
|
FieldEquinoctialOrbit<T> |
shiftedBy(double dt)
Get a time-shifted instance.
|
FieldEquinoctialOrbit<T> |
shiftedBy(T dt)
Get a time-shifted orbit.
|
EquinoctialOrbit |
toOrbit()
Transforms the FieldOrbit instance into an Orbit instance.
|
String |
toString()
Returns a string representation of this equinoctial parameters object.
|
static <T extends CalculusFieldElement<T>> |
trueToEccentric(T lv,
T ex,
T ey)
Computes the eccentric longitude argument from the true longitude argument.
|
fillHalfRow, fillHalfRow, fillHalfRow, fillHalfRow, fillHalfRow, fillHalfRow, getDate, getFrame, getJacobianWrtCartesian, getJacobianWrtParameters, getKeplerianMeanMotion, getKeplerianPeriod, getMu, getPVCoordinates, getPVCoordinates, getPVCoordinates, hasNonKeplerianAcceleration
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
interpolate
public FieldEquinoctialOrbit(T a, T ex, T ey, T hx, T hy, T l, PositionAngle type, Frame frame, FieldAbsoluteDate<T> date, T mu) throws IllegalArgumentException
a
- semi-major axis (m)ex
- e cos(ω + Ω), first component of eccentricity vectorey
- e sin(ω + Ω), second component of eccentricity vectorhx
- tan(i/2) cos(Ω), first component of inclination vectorhy
- tan(i/2) sin(Ω), second component of inclination vectorl
- (M or E or v) + ω + Ω, mean, eccentric or true longitude argument (rad)type
- type of longitude argumentframe
- the frame in which the parameters are defined
(must be a pseudo-inertial frame
)date
- date of the orbital parametersmu
- central attraction coefficient (m³/s²)IllegalArgumentException
- if eccentricity is equal to 1 or larger or
if frame is not a pseudo-inertial frame
public FieldEquinoctialOrbit(T a, T ex, T ey, T hx, T hy, T l, T aDot, T exDot, T eyDot, T hxDot, T hyDot, T lDot, PositionAngle type, Frame frame, FieldAbsoluteDate<T> date, T mu) throws IllegalArgumentException
a
- semi-major axis (m)ex
- e cos(ω + Ω), first component of eccentricity vectorey
- e sin(ω + Ω), second component of eccentricity vectorhx
- tan(i/2) cos(Ω), first component of inclination vectorhy
- tan(i/2) sin(Ω), second component of inclination vectorl
- (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 derivativeeyDot
- d(e sin(ω + Ω))/dt, second component of eccentricity vector derivativehxDot
- d(tan(i/2) cos(Ω))/dt, first component of inclination vector derivativehyDot
- d(tan(i/2) sin(Ω))/dt, second component of inclination vector derivativelDot
- d(M or E or v) + ω + Ω)/dr, mean, eccentric or true longitude argument derivative (rad/s)type
- type of longitude argumentframe
- the frame in which the parameters are defined
(must be a pseudo-inertial frame
)date
- date of the orbital parametersmu
- central attraction coefficient (m³/s²)IllegalArgumentException
- if eccentricity is equal to 1 or larger or
if frame is not a pseudo-inertial frame
public FieldEquinoctialOrbit(TimeStampedFieldPVCoordinates<T> pvCoordinates, Frame frame, T mu) throws IllegalArgumentException
The acceleration provided in pvCoordinates
is accessible using
FieldOrbit.getPVCoordinates()
and FieldOrbit.getPVCoordinates(Frame)
. All other methods
use mu
and the position to compute the acceleration, including
shiftedBy(CalculusFieldElement)
and FieldOrbit.getPVCoordinates(FieldAbsoluteDate, Frame)
.
pvCoordinates
- the position, velocity and accelerationframe
- the frame in which are defined the FieldPVCoordinates
(must be a pseudo-inertial frame
)mu
- central attraction coefficient (m³/s²)IllegalArgumentException
- if eccentricity is equal to 1 or larger or
if frame is not a pseudo-inertial frame
public FieldEquinoctialOrbit(FieldPVCoordinates<T> pvCoordinates, Frame frame, FieldAbsoluteDate<T> date, T mu) throws IllegalArgumentException
The acceleration provided in pvCoordinates
is accessible using
FieldOrbit.getPVCoordinates()
and FieldOrbit.getPVCoordinates(Frame)
. All other methods
use mu
and the position to compute the acceleration, including
shiftedBy(CalculusFieldElement)
and FieldOrbit.getPVCoordinates(FieldAbsoluteDate, Frame)
.
pvCoordinates
- the position end velocityframe
- the frame in which are defined the FieldPVCoordinates
(must be a pseudo-inertial frame
)date
- date of the orbital parametersmu
- central attraction coefficient (m³/s²)IllegalArgumentException
- if eccentricity is equal to 1 or larger or
if frame is not a pseudo-inertial frame
public FieldEquinoctialOrbit(FieldOrbit<T> op)
op
- orbital parameters to copypublic OrbitType getType()
getType
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getA()
Note that the semi-major axis is considered negative for hyperbolic orbits.
getA
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getADot()
Note that the semi-major axis is considered negative for hyperbolic orbits.
If the orbit was created without derivatives, the value returned is null.
getADot
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getEquinoctialEx()
getEquinoctialEx
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getEquinoctialExDot()
If the orbit was created without derivatives, the value returned is null.
getEquinoctialExDot
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getEquinoctialEy()
getEquinoctialEy
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getEquinoctialEyDot()
If the orbit was created without derivatives, the value returned is null.
getEquinoctialEyDot
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getHx()
getHx
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getHxDot()
If the orbit was created without derivatives, the value returned is null.
getHxDot
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getHy()
getHy
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getHyDot()
getHyDot
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getLv()
getLv
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getLvDot()
If the orbit was created without derivatives, the value returned is null.
getLvDot
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getLE()
getLE
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getLEDot()
If the orbit was created without derivatives, the value returned is null.
getLEDot
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getLM()
getLM
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getLMDot()
If the orbit was created without derivatives, the value returned is null.
getLMDot
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getL(PositionAngle type)
type
- type of the anglepublic T getLDot(PositionAngle type)
type
- type of the anglepublic boolean hasDerivatives()
hasDerivatives
in class FieldOrbit<T extends CalculusFieldElement<T>>
FieldOrbit.getADot()
,
FieldOrbit.getEquinoctialExDot()
,
FieldOrbit.getEquinoctialEyDot()
,
FieldOrbit.getHxDot()
,
FieldOrbit.getHyDot()
,
FieldOrbit.getLEDot()
,
FieldOrbit.getLvDot()
,
FieldOrbit.getLMDot()
,
FieldOrbit.getEDot()
,
FieldOrbit.getIDot()
public static <T extends CalculusFieldElement<T>> T eccentricToTrue(T lE, T ex, T ey)
T
- Type of the field elementslE
- = E + ω + Ω eccentric longitude argument (rad)ex
- first component of the eccentricity vectorey
- second component of the eccentricity vectorpublic static <T extends CalculusFieldElement<T>> T trueToEccentric(T lv, T ex, T ey)
T
- Type of the field elementslv
- = v + ω + Ω true longitude argument (rad)ex
- first component of the eccentricity vectorey
- second component of the eccentricity vectorpublic static <T extends CalculusFieldElement<T>> T meanToEccentric(T lM, T ex, T ey)
T
- Type of the field elementslM
- = M + ω + Ω mean longitude argument (rad)ex
- first component of the eccentricity vectorey
- second component of the eccentricity vectorpublic static <T extends CalculusFieldElement<T>> T eccentricToMean(T lE, T ex, T ey)
T
- Type of the field elementslE
- = E + ω + Ω mean longitude argument (rad)ex
- first component of the eccentricity vectorey
- second component of the eccentricity vectorpublic T getE()
getE
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getEDot()
If the orbit was created without derivatives, the value returned is null.
getEDot
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getI()
If the orbit was created without derivatives, the value returned is null.
getI
in class FieldOrbit<T extends CalculusFieldElement<T>>
public T getIDot()
getIDot
in class FieldOrbit<T extends CalculusFieldElement<T>>
protected TimeStampedFieldPVCoordinates<T> initPVCoordinates()
initPVCoordinates
in class FieldOrbit<T extends CalculusFieldElement<T>>
public FieldEquinoctialOrbit<T> shiftedBy(double dt)
dt
- time shift in secondspublic FieldEquinoctialOrbit<T> shiftedBy(T dt)
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.
shiftedBy
in interface FieldTimeShiftable<FieldOrbit<T extends CalculusFieldElement<T>>,T extends CalculusFieldElement<T>>
shiftedBy
in class FieldOrbit<T extends CalculusFieldElement<T>>
dt
- time shift in secondspublic FieldEquinoctialOrbit<T> interpolate(FieldAbsoluteDate<T> date, Stream<FieldOrbit<T>> sample)
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.
date
- interpolation datesample
- sample points on which interpolation should be doneprotected T[][] computeJacobianMeanWrtCartesian()
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.
computeJacobianMeanWrtCartesian
in class FieldOrbit<T extends CalculusFieldElement<T>>
FieldOrbit.computeJacobianEccentricWrtCartesian()
,
FieldOrbit.computeJacobianTrueWrtCartesian()
protected T[][] computeJacobianEccentricWrtCartesian()
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.
computeJacobianEccentricWrtCartesian
in class FieldOrbit<T extends CalculusFieldElement<T>>
FieldOrbit.computeJacobianMeanWrtCartesian()
,
FieldOrbit.computeJacobianTrueWrtCartesian()
protected T[][] computeJacobianTrueWrtCartesian()
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.
computeJacobianTrueWrtCartesian
in class FieldOrbit<T extends CalculusFieldElement<T>>
FieldOrbit.computeJacobianMeanWrtCartesian()
,
FieldOrbit.computeJacobianEccentricWrtCartesian()
public void addKeplerContribution(PositionAngle type, T gm, T[] pDot)
This method is used by integration-based propagators to evaluate the part of Keplerian motion to evolution of the orbital state.
addKeplerContribution
in class FieldOrbit<T extends CalculusFieldElement<T>>
type
- type of the position angle in the stategm
- attraction coefficient to usepDot
- 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)public String toString()
public EquinoctialOrbit toOrbit()
toOrbit
in class FieldOrbit<T extends CalculusFieldElement<T>>
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