Package org.orekit.orbits

Class 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 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​(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