Hamel Coefficients for the Rotational Motion of a Rigid Body

Abstract

A Lagrangian treatment of various forms of the rigid-body equations of motion is presented in this paper, including the most general expressions, which are the Boltzmann-Hamel equations. One key result that enables the derivations is the expression for the Hamel coefficients for the special case of rotational motion of a rigid body. The Hamel coefficients naturally arise in the Lagrange equations for quasi-coordinates. Another key result that enables the derivations is the expression for additional Hamel coefficients that arise when the translational-velocity vector of the mass center is coordinatized (expressed) along body-fixed axes. One interesting discovery is that the Boltzmann-Hamel equations are often misrepresented in standard textbooks. The misrepresentation stems from the fact that care is not exercised to distinguish the functional forms of the kinetic-energy expression.