Other way to look at rotation

Roll, Pitch, Yaw

Imagine three lines running through an airplane and intersecting at right angles at the airplane's center of gravity.

ROLL

PITCH

YAW

Rotation around the front-to-back

Rotation around the side-to-side axis

Rotation around the vertical axis

 

Euler Angles

written by Ian Humphrey <I.Humphrey@sct.gu.edu.au>

The Euler Angles (a, b, g) comprise a parametrisation of arbitrary rotations in three-dimensional space.
The description in this document coincides with that of "Angular Momentum in Quantum Mechanics" by Edmonds and "Angular Momentum" by Brink and Satchler, two standard texts in the field.

The effect of Euler angle rotation R=(a, b, g) is briefly as follows:
1. We start in frame S with cartesian axes, x, y and z.
2. We begin with a positive (anti-clockwise) rotation of magnitude a about the z axis of S. The resulting frame is called S'.
3. Next a positive rotation of magnitude b about the y' axis of frame S'. The resulting frame is called S''.
4. Finally a positive rotation of magnitude g about the z'' axis of S''. The resulting frame is called S'''.

the phycist definition :

STEP 1:
Rotation of a about z

STEP 2:
Rotation of b about y'

STEP 3:
Rotation of g about z''

Quaternions.