Stable Manifolds of Saddle Points for Pendulum Dynamics on S² and SO(3)

2011/03/15 by Taeyoung Lee, Lee, Taeyoung, Melvin Leok +3
Engineering · Mathematics · #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #Dynamics and Control of Mechanical Systems #FOS: Mathematics #Numerical methods for differential equations #math.DS

paper · pdf · doi:10.48550/arxiv.1103.2822

9 pages, 5 figures

arxiv created 2011/03/15 · openalex publication_date 2011/03/15 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Attitude control systems naturally evolve on nonlinear configuration spaces, such as S² and SO(3). The nontrivial topological properties of these configuration spaces 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 control systems on nonlinear spaces, and these global analysis techniques are applicable to a broad range of problems on nonlinear configuration manifolds.

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