Control of chaotic instabilities in a spinning spacecraft with dissipation using Lyapunovʹs method

Control of chaotic instability in a simplified model of a spinning spacecraft with dissipation is achieved using an algorithm derived using Lyapunovʹs second method. The control method is implemented on a realistic spacecraft parameter configuration which has been found to exhibit chaotic instability for a range of forcing amplitudes and frequencies when a sinusoidally varying torque is applied to the spacecraft. Such a torque, may arise in practice from an unbalanced rotor or from vibrations in appendages. Numerical simulations are performed and the results are studied by means of time history, phase space, Poincaré map, Lyapunov characteristic exponents and bifurcation diagrams.