Rodrigues Formula (Rodrigues Formula)
1. Cross multiplication of vectors
The meaning of the cross product of two vectors in 3d represents the area of a parallelogram.
direction and size
The cross product of two vectors can be written as an antisymmetric matrix and vector product
Vector triple product expansion:
Cross product distribution rate:
Second, the decomposition of the rotation vector
We can decompose v vv into two components parallel to the axis of rotation, and perpendicular to the axis of rotation, v ∥ and v ⊥.