| One important aspect of spacecraft attitude determination is the attitude acquisition maneuver. The attitude acquisition maneuver describes the transition of a spacecraft from an initial orbital insertion orientation to a final steady-state attitude. A damped, torque-free rigid body with an initial attitude about the minor principal mass moment of inertia axis is unstable but will reorient itself about the major principal mass moment of inertia axis. However, if the rigid body is additionally perturbed by non-dissipative factors then it may exhibit long-term chaotic behavior.;A complex spacecraft model which includes oscillating sub-bodies, a torsionally vibrating appendage, a viscously damped rotor, and a novel nonlinear controller is devised. Upon nondimensionalizing the equations of motion that describe the attitude dynamics of the spacecraft, the Melnikov criterion for chaos is constructed. I show that three principal types of motion that exist for the system: those that decay to a major axis spin equilibrium point, those that end up in a limit cycle and those that are chaotic. Lyapunov exponents show that the apparent chaotic trajectories are indeed chaotic. Two numerical techniques, parameter space evolution and phase space evolution, indicate that complex dynamics can occur for various spacecraft configurations and for various initial orientations. Using the method of generalized averaging with Jacobian elliptic functions it is shown that nonlinear phenomena are often preceded by instabilities of the principal and 1/2-subharmonic resonance frequencies. Bifurcation diagrams and cell maps clearly show that the complex behavior eventually dissipates. A spacecraft, however, can find itself in a limit cycle or a chaotic trajectory for an exceeding long period of time before dissipating to major axis spin. |
