Details

The equations for the velocity vector (a vertical unit vector in a laboratory frame relative to the positions of the axes of the body frame) are given by

,

,

,

and the Euler equations for the changes of angular momentum produced by the gravitational torque are

,

,

,

where is the angular velocity vector, the mass of the body, the acceleration of gravity, (a vector) represents the position of the center of gravity, and , , are the principal moments of inertia.

Reference

[1] T. Té́l and M. Gruiz, Chaotic Dynamics, An Introduction Based on Classical Mechanics, New York: Cambridge University Press, 2006.