1 Introduction
This article is meaningless without a clear definition and physical meaning of rotation . I once saw two different rotation representations about the θ angle around the z-axis in a book, and I also understand that rotation has different physical meanings in different fields, and even different application scenarios in the same field.
There are many representations of rotation: rotation matrices, Euler angles, quaternions, axis angles, Lie groups and Lie algebras. There are also many application scenarios for rotation: inertial navigation, robotics (manipulator kinematics, UAV attitude estimation, SLAM, etc.).
This article will use the rotation matrix as a carrier to illustrate the different situations of left multiplication and right multiplication of rotation (rotation matrix).
2. Background of this article
We first give the rotation matrix representation of the rotation around the x, y, z axes: 1
Among them, the positive direction of the rotation angle is given by the right-hand spiral rule. Note that for the rotation matrix that rotates around the Y axis, -sin is below.
In fact, regarding the above three matrices, different books and different library functions (such as different functions of matlab, makehgtform and angle2dcm) are not the same. The reason why we stipulate this is because of its physical meaning.
Take the z-axis rotation as an example:
2.1 The first physical meaning is the rotation of the coordinate system , and its application scenarios include SLAM, robotic arm kinematics, etc.
reference link
Rotation matrix to solve Euler angle Python implementation
Left multiplication and right multiplication of rotation - Zhihu (zhihu.com)