rotations

This module provides a mechanism for simple coordinate transformations. “Simple” here means coordinate tranformations which can be described as any number of serial rotations of a different coordinate frame about the x,y, or z axes.

There are many subtleties involved in describing coordinate rotation mathematically (https://en.wikipedia.org/wiki/Rotation_matrix#Ambiguities)

This module aims to emulate the convention used in the Vallado textbook:

  • Rotations are of the coordinate system “underneath” the vector (vector stays fixed, axes move)
  • Rotation matrices ( M ) are of the “pre-multiplication” type ( Mv, with v a column vector )

API

geospacepy.rotations.rot(angles, axis, vecs)[source]

Return representation of 3-component vectors vecs in a coordinate systems which has been rotated an angle (angle), about axis (axis)

Parameters:
  • angles (float or np.ndarray) – The angle(s) (in radians) which the coordinate system will be rotated by. For single float values, all vecs will be rotated by the same angle
  • axis (int) – The axis (0,1,2) about which to rotate the coordinate system
  • vecs (np.ndarray) – Array of n 3-component vectors for which the components in the rotated coordinate frame will be returned (shape=(n,3))
Returns:

rotated_vecs – The components of vecs in the rotated frame (shape=(n,3))
Return type:

np.ndarray
geospacepy.rotations.rot1(angles, vecs)[source]

Shorthand for rotation about axis 0 (x / I / e1)

geospacepy.rotations.rot2(angles, vecs)[source]

Shorthand for rotation about axis 1 (y / J / e2)

geospacepy.rotations.rot3(angles, vecs)[source]

Shorthand for rotation about axis 2 (z / K / e3)

geospacepy.rotations.rotmat(angle, axis)[source]

Return 3x3 elementary rotation matrix (M), which when pre-multiplied (M * v) by a 3x1 column vector (v) returns the new components of v in a coordinate system which has been rotated through an angle (angle) in radians about axis (axis), relative to the vector’s native coordinate system

Parameters:
  • angle (float) – The angle (in radians) to rotate the coordinate axes by
  • axis (int) – The axis (0,1,2) about which the rotation should be performed
Returns:

M – The rotation matrix
Return type:

np.ndarray, shape=(3,3)

Notes

Positive angles represent rotations according the the right hand rule (the directions of the fingers if the thumb is the axis)