Attitude Dynamics of Orbiting Gyrostats

Abstract

Equilibrium attitudes of a rigid satellite with N rotors in a central gravitational field are investigated. The equations of motion are written as a noncanonical Hamiltonian system, where the Hamiltonian includes the potential, a volume integral over the body of the gyrostat. In practice, the Hamiltonian is approximated to partially decouple the position and attitude equations. The equilibria of this system of equations represent the steady motions of the body as seen in the body frame, and correspond to stationary points of the Hamiltonian constrained by the Casimir functions. This defines an algorithm for computing equilibria. In contrast to other approaches, this algorithm provides stability information directly, since the calculations required to solve the constrained minimization problem are also involved in computing the positive definiteness of the Hamiltonian as a Lyapunov function.