What does rotation matrix mean?
A 2 by 2 matrix of the sine and cosine of the heading that turns a vector in the body frame into the same vector in the world frame. It never changes a vector's length, and its inverse is its transpose, the rotation by minus the heading.
In a lesson
Two facts make this pleasant. A rotation matrix's inverse is its transpose, so no division is ever needed. And a rotation never changes a vector's length, so
hypot(vx, vy)is the same in both frames. That last one is a useful check in code: if the length changed, the maths is wrong.
Learn it
- Taught in U2.2 The rotation matrix Kinematics and frames, University