Rotations

A rotation is a circular movement of an object around a center (or point) of rotation. A three-dimensional object always rotates around an imaginary line called a rotation axis. If the axis passes through the body's center of mass, the body is said to rotate upon itself, or spin.

    In daily Life we see or experience rotations everywhere such as:

• In computer animation
   and robotics
• Joint angles, rigid body orientations,
  camera parameters
• 2D or 3D

Euler rotation

Euler rotations provide an alternative description of a rotation. It is a composition of three rotations defined as the movement obtained by changing one of the Euler angles while leaving the other two constant. Euler rotations are never expressed in terms of the external frame, or in terms of the co-moving rotated body frame, but in a mixture. They constitute a mixed axes of rotation system, where the first angle moves the line of nodes around the external axis z, the second rotates around the line of nodes and the third one is an intrinsic rotation around an axis fixed in the body that moves.

These rotations are called precession, nutation, and intrinsic rotation.

Euler Angles

1. Yaw
rotate around y-axis

2. Pitch
rotate around (rotated) x-axis

3. Roll
rotate around (rotated) y-axis