Chaotic attitude tumbling of an asymmetric gyrostat in a gravitational field

Abstract

The chaotic attitude tumbling of an asymmetric gyrostat is investigated in detail. The gyrostat has three symmetrical wheels along the principal axes rotation about a fixed point under the action of either the gravity torques transformed into Hamiltonian form. This makes the Poincare ́–Melnikov–Arnold (PAM) function developed by Holmes and Marsden applicable. The physical parameters triggering the chaotic attitude are established. The analytical results are checked by using the fourth-order Bunge-Kutta simulation in terms of the Eular parameters (quaternions). The relationships of the following physical parameters are established: moments of intertia of Carriers and wheels, positions of the mass center, kinetic energy and moment of momentum of the torque-free gyrostat, and initial attitude leading to chaotic motion. The results show that the PAM function is a powerful analytical tool for the treatment of the dynamics of nonlinear gyrostat orientations.