``element_conversion`` ====================== Functions for converting between sets of orbital elements. This module provide a variety of functions and classes to convert between different representations of translational and rotational states (e.g. Cartesian ↔ Keplerian). .. note:: Rotations between different reference frames are provided in the :ref:`\`\`frame_conversion\`\`` module. Notes ----- Unless specified otherwise, the Keplerian elements are ordered as: +-------+---------------------------------------------------------------------------------------+ | Index | Keplerian Element | +-------+---------------------------------------------------------------------------------------+ | ``0`` | Semi-major axis (except if eccentricity = ``1.0``, then represents semi-latus rectum) | +-------+---------------------------------------------------------------------------------------+ | ``1`` | Eccentricity | +-------+---------------------------------------------------------------------------------------+ | ``2`` | Inclination | +-------+---------------------------------------------------------------------------------------+ | ``3`` | Argument of periapsis | +-------+---------------------------------------------------------------------------------------+ | ``4`` | Longitude of ascending node | +-------+---------------------------------------------------------------------------------------+ | ``5`` | True anomaly | +-------+---------------------------------------------------------------------------------------+ Unless specified otherwise, the spherical elements are ordered as: +-------+--------------------------------------------------------------------------------------+ | Index | Spherical State Element | +-------+--------------------------------------------------------------------------------------+ | ``0`` | Radial distance | +-------+--------------------------------------------------------------------------------------+ | ``1`` | Latitude | +-------+--------------------------------------------------------------------------------------+ | ``2`` | Longitude | +-------+--------------------------------------------------------------------------------------+ | ``3`` | Speed | +-------+--------------------------------------------------------------------------------------+ | ``4`` | Flight-path angle | +-------+--------------------------------------------------------------------------------------+ | ``5`` | Heading angle | +-------+--------------------------------------------------------------------------------------+ Unless specified otherwise, the Modified equinoctial elements (MEE; see `here `_, element set *k*) are ordered as follows. The element :math:`I`, which defines the location of the MEE singularity is not treated as a state element, but is provided/determined separately: +-------+--------------------------------------------------------------------------------------+ | Index | Modified equinoctial Element | +-------+--------------------------------------------------------------------------------------+ | ``0`` | Semi-parameter | +-------+--------------------------------------------------------------------------------------+ | ``1`` | f-element | +-------+--------------------------------------------------------------------------------------+ | ``2`` | g-element | +-------+--------------------------------------------------------------------------------------+ | ``3`` | h-element | +-------+--------------------------------------------------------------------------------------+ | ``4`` | k-element | +-------+--------------------------------------------------------------------------------------+ | ``5`` | True longitude | +-------+--------------------------------------------------------------------------------------+ Functions --------- .. currentmodule:: tudatpy.astro.element_conversion .. autosummary:: cartesian_to_keplerian keplerian_to_cartesian keplerian_to_cartesian_elementwise mean_to_true_anomaly true_to_mean_anomaly true_to_eccentric_anomaly eccentric_to_true_anomaly eccentric_to_mean_anomaly mean_to_eccentric_anomaly elapsed_time_to_delta_mean_anomaly delta_mean_anomaly_to_elapsed_time mean_motion_to_semi_major_axis semi_major_axis_to_mean_motion keplerian_to_mee_manual_singularity keplerian_to_mee flip_mee_singularity mee_to_keplerian cartesian_to_mee cartesian_to_mee_manual_singularity mee_to_cartesian quaternion_entries_to_rotation_matrix rotation_matrix_to_quaternion_entries cartesian_to_spherical spherical_to_cartesian spherical_to_cartesian_elementwise .. autofunction:: tudatpy.astro.element_conversion.cartesian_to_keplerian .. autofunction:: tudatpy.astro.element_conversion.keplerian_to_cartesian .. autofunction:: tudatpy.astro.element_conversion.keplerian_to_cartesian_elementwise .. autofunction:: tudatpy.astro.element_conversion.mean_to_true_anomaly .. autofunction:: tudatpy.astro.element_conversion.true_to_mean_anomaly .. autofunction:: tudatpy.astro.element_conversion.true_to_eccentric_anomaly .. autofunction:: tudatpy.astro.element_conversion.eccentric_to_true_anomaly .. autofunction:: tudatpy.astro.element_conversion.eccentric_to_mean_anomaly .. autofunction:: tudatpy.astro.element_conversion.mean_to_eccentric_anomaly .. autofunction:: tudatpy.astro.element_conversion.elapsed_time_to_delta_mean_anomaly .. autofunction:: tudatpy.astro.element_conversion.delta_mean_anomaly_to_elapsed_time .. autofunction:: tudatpy.astro.element_conversion.mean_motion_to_semi_major_axis .. autofunction:: tudatpy.astro.element_conversion.semi_major_axis_to_mean_motion .. autofunction:: tudatpy.astro.element_conversion.keplerian_to_mee_manual_singularity .. autofunction:: tudatpy.astro.element_conversion.keplerian_to_mee .. autofunction:: tudatpy.astro.element_conversion.flip_mee_singularity .. autofunction:: tudatpy.astro.element_conversion.mee_to_keplerian .. autofunction:: tudatpy.astro.element_conversion.cartesian_to_mee .. autofunction:: tudatpy.astro.element_conversion.cartesian_to_mee_manual_singularity .. autofunction:: tudatpy.astro.element_conversion.mee_to_cartesian .. autofunction:: tudatpy.astro.element_conversion.quaternion_entries_to_rotation_matrix .. autofunction:: tudatpy.astro.element_conversion.rotation_matrix_to_quaternion_entries .. autofunction:: tudatpy.astro.element_conversion.cartesian_to_spherical .. autofunction:: tudatpy.astro.element_conversion.spherical_to_cartesian .. autofunction:: tudatpy.astro.element_conversion.spherical_to_cartesian_elementwise