Stable manifolds of saddle equilibria for pendulum dynamics on S2 and SO(3)

Attitude control systems naturally evolve on nonlinear configurations, such as S² and SO(3). The nontrivial topological properties of these configurations result in interesting and complicated nonlinear dynamics when studying the corresponding closed loop attitude control systems. In this paper, we review some global analysis and simulation techniques that allow us to describe the global nonlinear stable manifolds of the hyperbolic equilibria of these closed loop systems. A deeper understanding of these invariant manifold structures are critical to understanding the global stabilization properties of closed loop attitude control systems, and these global analysis techniques are applicable to a broad range of problems on nonlinear configuration manifolds.