  Euler's equation relates the change in angular momentum of a rigid body to
the applied torque. This paper fills a gap in the literature by using
Lagrangian dynamics to derive Euler's equation in terms of generalized
coordinates. This is done by parameterizing the angular velocity vector in
terms of 3-2-1 and 3-1-3 Euler angles as well as Euler parameters, that is,
unit quaternions.
