Control of Chaotic Instability in a Dual-Spin Spacecraft with Dissipation Using Energy Methods

Control of chaotic instability in a rotating multibody system in theform of a dual-spin spacecraft with an axial nutational damper isachieved using an algorithm derived using energy methods. The controlmethod is implemented on two realistic spacecraft parameterconfigurations which have been found to exhibit chaotic instability whena sinusoidally varying torque is applied to the spacecraft for a rangeof forcing amplitudes and frequencies. Such a torque, in practice, mayarise under malfunction of the control system or from an unbalancedrotor. Chaotic instabilities arising from these torques could introduceuncertainties and irregularities into a spacecraft's attitude andconsequently impair pointing accuracy. The control method is formulatedfrom nutational stability results derived using an energy sinkapproximation for a dual-spin spacecraft with an asymmetric platform andaxisymmetric rotor. The effectiveness of the control method is shownnumerically and the results are studied by means of time history, phasespace, Poincar'e map, Lyapunov characteristic exponents and Bifurcationdiagrams.