:mod:`lamberthub.utils.angles`
==============================

.. py:module:: lamberthub.utils.angles
   :noindex:

.. autoapi-nested-parse::

   Utilities related to angles computations



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


Functions
~~~~~~~~~

.. autoapisummary::


   lamberthub.utils.angles.get_transfer_angle


   lamberthub.utils.angles.get_orbit_normal_vector


   lamberthub.utils.angles.get_orbit_inc_and_raan_from_position_vectors


   lamberthub.utils.angles.nu_to_E


   lamberthub.utils.angles.E_to_nu


   lamberthub.utils.angles.nu_to_B


   lamberthub.utils.angles.B_to_nu


   lamberthub.utils.angles.nu_to_H


   lamberthub.utils.angles.H_to_nu



.. py:function:: get_transfer_angle(r1, r2, prograde)

   Solves for the transfer angle being known the sense of rotation.

   :param r1: Initial position vector.
   :type r1: np.array
   :param r2: Final position vector.
   :type r2: np.array
   :param prograde: If True, it assumes prograde motion, otherwise assumes retrograde.
   :type prograde: bool

   :returns: **dtheta** -- Transfer angle in radians.
   :rtype: float


.. py:function:: get_orbit_normal_vector(r1, r2, prograde)

   Computes a unitary normal vector aligned with the specific angular momentum
   one of the orbit.

   :param r1: Initial position vector.
   :type r1: np.array
   :param r2: Final position vector.
   :type r2: np.array
   :param prograde: If True, it assumes prograde motion, otherwise assumes retrograde.
   :type prograde: bool

   :returns: **i_h** -- Unitary vector aligned with orbit specific angular momentum.
   :rtype: np.array


.. py:function:: get_orbit_inc_and_raan_from_position_vectors(r1, r2, prograde)

   Computes the inclination of the orbit being known an initial and a final
   position vectors together with the sense of motion.

   :param r1: Initial position vector.
   :type r1: np.array
   :param r2: Final position vector.
   :type r2: np.array
   :param prograde: If True, it assumes prograde motion, otherwise assumes retrograde.
   :type prograde: bool

   :returns: * **inc** (*float*) -- Inclination of the orbit.
             * **raan** (*float*) -- Right ascension of the ascending node.


.. py:function:: nu_to_E(nu, ecc)

   Retrieves eccentric anomaly from true one.

   :param nu: True anomaly.
   :type nu: float
   :param ecc: Eccentricity of the orbit.
   :type ecc: float

   :returns: **E** -- Eccentric anomaly.
   :rtype: float


.. py:function:: E_to_nu(E, ecc)

   Retrieves true anomaly from eccentric one.

   :param E: Eccentric anomaly.
   :type E: float
   :param ecc: Eccentricity of the orbit.
   :type ecc: float

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


.. py:function:: nu_to_B(nu)

   Retrieves parabolic anomaly from true one.

   :param nu: True anomaly
   :type nu: float

   :returns: **B** -- Parabolic anomaly
   :rtype: float

   .. rubric:: Notes

   As explained in Vallado's [1], :math:`B` is used instead of :math:`P` just
   to not confuse with the orbital parameter.


.. py:function:: B_to_nu(B)

   Retrieves the true anomaly from parabolic one.

   :param B: Parabolic anomaly
   :type B: float

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

   .. rubric:: Notes

   As explained in Vallado's [1], :math:`B` is used instead of :math:`P` just
   to not confuse with the orbital parameter.


.. py:function:: nu_to_H(nu, ecc)

   Retrieves hyperbolic anomaly from true one.

   :param nu: True anomaly
   :type nu: float
   :param ecc: Eccentricity of the orbit
   :type ecc: float

   :returns: **H** -- Hyperbolic anomaly
   :rtype: float


.. py:function:: H_to_nu(H, ecc)

   Retrieves hyperbolic anomaly from true one.

   :param H: Hyperbolic anomaly
   :type H: float
   :param ecc: Eccentricity of the orbit
   :type ecc: float

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