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 frame_conversion module.

Notes#

In general, 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

Functions#

cartesian_to_keplerian(cartesian_elements, ...)

Convert Cartesian to Keplerian elements.

keplerian_to_cartesian(keplerian_elements, ...)

Convert Keplerian elements to Cartesian.

keplerian_to_cartesian_elementwise(...)

Convert Keplerian elements to Cartesian, with elementwise input.

quaternion_entries_to_rotation_matrix(...)

Converts an array of four quaternion elements to the equivalent rotation matrix.

rotation_matrix_to_quaternion_entries(...)

Converts a rotation matrix to the equivalent array of four quaternion elements.
cartesian_to_keplerian(cartesian_elements: numpy.ndarray[numpy.float64[6, 1]], gravitational_parameter: float) → numpy.ndarray[numpy.float64[6, 1]]#

Convert Cartesian to Keplerian elements.

Note

See module level documentation for the standard ordering convention of Keplerian elements used.

Parameters

  • cartesian_elements (numpy.ndarray) – Cartesian state that is to be converted to Keplerian elements

  • gravitational_parameter (float) – Gravitational parameter of central body used for conversion

Returns

Keplerian elements, as computed from Cartesian element input.

Return type

numpy.ndarray

keplerian_to_cartesian(keplerian_elements: numpy.ndarray[numpy.float64[6, 1]], gravitational_parameter: float) → numpy.ndarray[numpy.float64[6, 1]]#

Convert Keplerian elements to Cartesian.

Note

See module level documentation for the standard ordering convention of Keplerian elements used.

Parameters

  • keplerian_elements (numpy.ndarray) – Keplerian state that is to be converted to Cartesian elements

  • gravitational_parameter (float) – Gravitational parameter of central body used for conversion

Returns

Keplerian elements, as computed from Cartesian element input.

Return type

numpy.ndarray

keplerian_to_cartesian_elementwise(semi_major_axis: float, eccentricity: float, inclination: float, argument_of_periapsis: float, longitude_of_ascending_node: float, true_anomaly: float, gravitational_parameter: float) → numpy.ndarray[numpy.float64[6, 1]]#

Convert Keplerian elements to Cartesian, with elementwise input.

Note

The final Keplerian element is always the true anomaly.

Parameters

  • semi_major_axis (float) – Semi-major axis (except if eccentricity = 1.0, then represents semi-latus rectum)

  • eccentricity (float) – Eccentricity

  • inclination (float) – Inclination

  • argument_of_periapsis (float) – Argument of periapsis

  • longitude_of_ascending_node (float) – Longitude of ascending node

  • true_anomaly (float) – True anomaly

  • gravitational_parameter (float) – Gravitational parameter of central body used for conversion

Returns

Keplerian elements, as computed from Cartesian element input.

Return type

numpy.ndarray

quaternion_entries_to_rotation_matrix(quaternion_entries: numpy.ndarray[numpy.float64[4, 1]]) → numpy.ndarray[numpy.float64[3, 3]]#

Converts an array of four quaternion elements to the equivalent rotation matrix.

Function to convert an array of four quaternion elements to the equivalent rotation matrix. These quaternion elements are for instance used when propagating rotational dynamics in Tudat, and this function can be used to convert the numerical results to a usable rotation matrix. See our user guide for more details.

Parameters

quaternion_entries (numpy.ndarray) – Quaternion elements, as per the convention used in the Eigen library

Returns

Rotation matrix defining the equivalent rotation.

Return type

numpy.ndarray

rotation_matrix_to_quaternion_entries(rotation_matrix: numpy.ndarray[numpy.float64[3, 3]]) → numpy.ndarray[numpy.float64[4, 1]]#

Converts a rotation matrix to the equivalent array of four quaternion elements.

Inverse function of quaternion_entries_to_rotation_matrix().

Parameters

rotation_matrix (numpy.ndarray) – Rotation matrix

Returns

Equivalent quaternion elements, as per the convention used in the Eigen library

Return type

numpy.ndarray