boinor.core.propagation.farnocchia
==================================

.. py:module:: boinor.core.propagation.farnocchia


Functions
---------

.. autoapisummary::

   boinor.core.propagation.farnocchia.S_x
   boinor.core.propagation.farnocchia.dS_x_alt
   boinor.core.propagation.farnocchia.d2S_x_alt
   boinor.core.propagation.farnocchia.D_to_M_near_parabolic
   boinor.core.propagation.farnocchia.M_to_D_near_parabolic
   boinor.core.propagation.farnocchia.delta_t_from_nu
   boinor.core.propagation.farnocchia.nu_from_delta_t
   boinor.core.propagation.farnocchia.farnocchia_coe
   boinor.core.propagation.farnocchia.farnocchia_rv


Module Contents
---------------

.. py:function:: S_x(ecc, x, atol=1e-12)

.. py:function:: dS_x_alt(ecc, x, atol=1e-12)

.. py:function:: d2S_x_alt(ecc, x, atol=1e-12)

.. py:function:: D_to_M_near_parabolic(D, ecc)

.. py:function:: M_to_D_near_parabolic(M, ecc, tol=1.48e-08, maxiter=50)

   Parabolic eccentric anomaly from mean anomaly, near parabolic case.

   :param M: Mean anomaly in radians.
   :type M: float
   :param ecc: Eccentricity (~1).
   :type ecc: float
   :param tol: Absolute tolerance for Newton convergence.
   :type tol: float, optional
   :param maxiter: Maximum number of iterations for Newton convergence.
   :type maxiter: int, optional

   :returns: **D** -- Parabolic eccentric anomaly.
   :rtype: float


.. py:function:: delta_t_from_nu(nu, ecc, k=1.0, q=1.0, delta=0.01)

   Time elapsed since periapsis for given true anomaly.

   :param nu: True anomaly.
   :type nu: float
   :param ecc: Eccentricity.
   :type ecc: float
   :param k: Gravitational parameter.
   :type k: float
   :param q: Periapsis distance.
   :type q: float
   :param delta: Parameter that controls the size of the near parabolic region.
   :type delta: float

   :returns: **delta_t** -- Time elapsed since periapsis.
   :rtype: float


.. py:function:: nu_from_delta_t(delta_t, ecc, k=1.0, q=1.0, delta=0.01)

   True anomaly for given elapsed time since periapsis.

   :param delta_t: Time elapsed since periapsis.
   :type delta_t: float
   :param ecc: Eccentricity.
   :type ecc: float
   :param k: Gravitational parameter.
   :type k: float
   :param q: Periapsis distance.
   :type q: float
   :param delta: Parameter that controls the size of the near parabolic region.
   :type delta: float

   :returns: **nu** -- True anomaly.
   :rtype: float


.. py:function:: farnocchia_coe(k, p, ecc, inc, raan, argp, nu, tof)

.. py:function:: farnocchia_rv(k, r0, v0, tof)

   Propagates orbit using mean motion.

   This algorithm depends on the geometric shape of the orbit.
   For the case of the strong elliptic or strong hyperbolic orbits:

   ..  math::

       M = M_{0} + \frac{\mu^{2}}{h^{3}}\left ( 1 -e^{2}\right )^{\frac{3}{2}}t

   .. versionadded:: 0.9.0

   :param k: Standar Gravitational parameter
   :type k: float
   :param r0: Initial position vector wrt attractor center.
   :type r0: numpy.ndarray
   :param v0: Initial velocity vector.
   :type v0: numpy.ndarray
   :param tof: Time of flight (s).
   :type tof: float

   .. rubric:: Notes

   This method takes initial :math:`\vec{r}, \vec{v}`, calculates classical orbit parameters,
   increases mean anomaly and performs inverse transformation to get final :math:`\vec{r}, \vec{v}`
   The logic is based on formulae (4), (6) and (7) from http://dx.doi.org/10.1007/s10569-013-9476-9