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r3f: Rotation of 3-dimensional Reference Frames

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posted on 2025-02-05, 13:25 authored by David WoodburnDavid Woodburn

The `r3f` library includes attitude-representation conversions, reference-frame conversions, and rotation matrix (direction cosine matrix) utilities. All twenty possible conversions among the following five attitude representations are provided: rotation vector, rotation axis and angle, roll and pitch and yaw (RPY) Euler angles, direction cosine matrix (DCM), and quaternion. This library also includes all twelve possible conversions among the following four frames: ECEF (Earth-centered, Earth-fixed), geodetic (latitude, longitude, and height above ellipsoid), local-level tangent, and local-level curvilinear. Both local-level frames can be in either NED (North, East, Down) or ENU (East, North, Up) orientation. A general `dcm` function will generate any arbitrary rotation matrix based on an arbitrary sequence of Euler rotation angles. This can be used to convert between ECEF and ECI (Earth-centered Inertial) frames.

A few additional utility functions are included. The `orthonormalize_dcm` function will normalize and orthogonalize a rotation matrix. The two Rodrigues's rotation functions, `rodrigues_rotation` and `inverse_rodrigues_rotation`, are meant for converting a vector to the matrix exponential of the skew-symmetric matrix of that vector and back again.

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