Asymptotic stability of rigid body attitude systems

A rigid body, supported by a fixed pivot point, is free to rotate in three dimensions. Two cases are studied: the balanced case, whose dynamics are described by the Euler equations for a free rigid body, and the unbalanced case, whose dynamics are described by the heavy top equations. Both cases include linear passive dissipation effects. For each case, conditions are presented that guarantee asymptotic stability for relevant equilibrium solutions. The developments are based on a careful treatment of nonlinear coupling in applying LaSalle´s invariance principle. Emphases are given to the partial damping cases; an approach based on the polynomial structure of the dynamics is used to obtain asymptotic stability conditions for these cases.