2007/07/09 by Nalin A. Chaturvedi, Chaturvedi, Nalin A., Taeyoung Lee +5
Engineering · Mathematics · Physics and Astronomy · #Control and Dynamics of Mobile Robots #Control and Stability of Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #math.DS
paper · pdf · doi:10.48550/arxiv.0707.1196
22 pages, 2 figures
arxiv created 2007/07/09 · openalex publication_date 2007/07/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the spherical 2D pendulum models as special cases. The case where the rigid body is asymmetric and the center of mass is distinct from the pivot location leads to the 3D pendulum. Full and reduced 3D pendulum models are introduced and used to study important features of the nonlinear dynamics: conserved quantities, equilibria, invariant manifolds, local dynamics near equilibria and invariant manifolds, and the presence of chaotic motions. These results demonstrate the rich and complex dynamics of the 3D pendulum.