Package org.orekit.orbits

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

  • All Implemented Interfaces:
    FieldTimeInterpolable<FieldOrbit<T>,​T>, FieldTimeShiftable<FieldOrbit<T>,​T>, FieldTimeStamped<T>, FieldPVCoordinatesProvider<T>
    public class FieldEquinoctialOrbit<T extends org.hipparchus.RealFieldElement<T>>
extends FieldOrbit<T>
    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.

    Since:
    9.0
    Author:
    Mathieu Roméro, Luc Maisonobe, Guylaine Prat, Fabien Maussion, Véronique Pommier-Maurussane
    See Also:
    Orbit, KeplerianOrbit, CircularOrbit, CartesianOrbit

    • 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

      • 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

      • 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)

      • getL

        public T getL​(PositionAngle type)
        Get the longitude argument.
        Parameters:
        type - type of the angle
        Returns:
        longitude argument (rad)

      • getLDot

        public T getLDot​(PositionAngle type)
        Get the longitude argument derivative.
        Parameters:
        type - type of the angle
        Returns:
        longitude argument derivative (rad/s)

      • eccentricToTrue

        public static <T extends org.hipparchus.RealFieldElement<T>> T eccentricToTrue​(T lE,
                                                                               T ex,
                                                                               T ey)
        Computes the true longitude argument from the eccentric longitude argument.
        Type Parameters:
        T - Type of the field elements
        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 <T extends org.hipparchus.RealFieldElement<T>> T trueToEccentric​(T lv,
                                                                               T ex,
                                                                               T ey)
        Computes the eccentric longitude argument from the true longitude argument.
        Type Parameters:
        T - Type of the field elements
        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 <T extends org.hipparchus.RealFieldElement<T>> T meanToEccentric​(T lM,
                                                                               T ex,
                                                                               T ey)
        Computes the eccentric longitude argument from the mean longitude argument.
        Type Parameters:
        T - Type of the field elements
        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 <T extends org.hipparchus.RealFieldElement<T>> T eccentricToMean​(T lE,
                                                                               T ex,
                                                                               T ey)
        Computes the mean longitude argument from the eccentric longitude argument.
        Type Parameters:
        T - Type of the field elements
        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 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)

      • 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 FieldEquinoctialOrbit<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 FieldEquinoctialOrbit<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 FieldEquinoctialOrbit<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 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 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 equinoctial parameters 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 EquinoctialOrbit 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