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Attitude control systems naturally evolve on nonlinear configuration spaces,such as S^2 and SO(3). The nontrivial topological properties of theseconfiguration spaces result in interesting and complicated nonlinear dynamicswhen studying the corresponding closed loop attitude control systems. In thispaper, we review some global analysis and simulation techniques that allow usto describe the global nonlinear stable manifolds of the hyperbolic equilibriaof these closed loop systems. A deeper understanding of these invariantmanifold structures are critical to understanding the global stabilizationproperties of closed loop control systems on nonlinear spaces, and these globalanalysis techniques are applicable to a broad range of problems on nonlinearconfiguration manifolds.

Stable Manifolds of Saddle Points for Pendulum Dynamics on S^2 and SO(3)