A multibody analog of the dual-spin problem

A version of the Euler-Lagrange equation for motions on the special orthogonal group SO(3) is established from the invariant form of the Lagrange-D´Alembert principle. This scheme can be used to derive dynamical equations for many-rigid-body problems. It can also be applied to certain continuum mechanical problems, e.g., the special Cosserat rod. The method is applied to a multibody analog of the classical dual-spin problem and the dynamical equations are obtained. It is then shown that, with a suitable damping mechanism on one body and on the joint, an asymptotic stability theorem can be proved by using the LaSalle invariance principle. The driven rotor momenta are shown to play an important role in attitude acquisition