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### 8.3 Rotation

— Function: antik:euler-angle-rotation rot3a rot1 rot3b &optional passive

Compute the matrix for a `3-1-3` rotation. See Curtis (9.118).

— Function: antik:rotate angle &optional passive

Create a rotation matrix in two dimensions. Passive rotation if passive is true, otherwise active.

— Function: antik:rotate-3d axis angle &optional passive

Create a rotation matrix about the (0, `1`, 2) axis in three dimensions. Passive rotation if passive is true, otherwise active.

— Function: antik:rotate-3daa rotation-axis angle &optional passive

Rotation about an arbitrary axis in `3d`. See Goldstein, Poole, Safko (4.62) or http://mathworld.wolfram.com/RotationFormula.html.

— Function: antik:tait-bryan-angles dcm

Find the three angles psi, theta, phi of a `3-2-1` (Tait-Bryan) rotation for the direction cosine matrix.

— Function: antik:tait-bryan-rotation rot1 rot2 rot3 &optional passive

Compute the matrix for a `3-2-1` (yaw-pitch-roll) rotation. See Curtis (9.124). This transforms a vector in the body frame into a vector in the external frame.