This lecture extends the concept of rotation matrices from 2D to 3D, introducing the special orthogonal group in three dimensions and the right-hand rule for defining axes and rotation directions. It also discusses the importance of rotation order, the concept of gimbal lock, and how to extract roll, pitch, and yaw angles from a rotation matrix.

This chapter extends the concept of the rotation matrix from two dimensions to three dimensions, incorporating the Z-axis. It explains the properties of the special orthogonal group in three dimensions and introduces the right-hand rule for defining elementary rotations about each axis.

The chapter discusses Euler angles and Cardan angles, which are methods of representing rotations in three-dimensional space. It explains the importance of the order of rotations and demonstrates that rotation matrices are not commutative, meaning the sequence of rotations affects the final orientation.

This chapter discusses the problem of gimbal lock when working with roll, pitch, and yaw angles in 3D rotations. It explains how gimbal lock occurs when the pitch angle is ±π/2, making it impossible to distinguish between roll and yaw angles, and suggests ways to avoid this issue.