This video covers the principal rotations (x, y and z axes) and their matrices that form euler angle sequences. This builds on the previous video that covers that intuition why rotation matrices are formulated the way they are with the example of a principal z rotation.
In essence, the column vectors of a 3D rotation matrix tell you where the principal basis vectors will end up after applying the rotation. So for a rotation about the Z axis, the 3rd column vector of the rotation matrix will be [ 0, 0, 1 ], because when you are rotating about the Z axis, the Z axis remains stationary.
This video also covers how euler angle sequences are defined, and how the order of the rotations affect the final orientation of the rotated reference frame. Again, this video is a prerequisite for the next video that will go over in greater detail what euler angles are and how they are used in real life scenarios (spacecraft, airplanes, drones, robots).
#eulerangles #principalrotations #numericalmethods
