1. Internal rotation and external rotation
The conversion relationship between internal rotation and external rotation: the results of the two are the same if the positions of the first and third rotations are interchanged. For example the inner rotation of a ZYX rotation and the outer rotation of an XYZ rotation have the same rotation matrix.
1. Rotation around fixed axis XYZ (RPY angle) (external rotation)
Assume that there are two coordinate systems A and B, which coincide completely initially. The process is as follows: B rotates around A's X axis by γ angle, then around A's Y axis by β angle, and finally around A's Z axis by α angle to complete the rotation. During the whole process, A does not move and B moves.
The calculation method of the rotation matrix is as follows: R = Rz * Ry *Rx, multiplication order: from right to left, rotate the X-axis, Y-axis, and Z-axis in turn. Among them, cα = cosα, sα = sinα, matrix multiplication, the results are as follows:
2. Rotate around the axis ZYX (Euler angle) (internal rotation)
The process is as follows: B rotates around B's Z axis by α angle, then around B's Y axis by β angle, and finally around B's X axis by γ angle to complete the rotation. During the whole process, A does not move and B moves. The rotation matrix is calculated as follows: R = Rz * Ry *Rx. Multiplication order: left to right
