Stability by KAM confinement of certain wild, nongeneric relative equilibria of underwater vehicles with coincident centers of mass and bouyancy

2002/04/02 by George W. Patrick, Patrick, George W.
Engineering · Mathematics · Physics and Astronomy · #Control and Dynamics of Mobile Robots #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics Simulations and Interactions #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG) #math-ph #math.DS #math.MP #math.SG

paper · pdf · doi:10.48550/arxiv.math/0204028

18 pages, 3 figures

arxiv created 2002/04/02 · openalex publication_date 2002/04/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Purely rotational relative equilibria of an ellipsoidal underwater vehicle occur at nongeneric momentum where the symplectic reduced spaces change dimension. The stability these relative equilibria under momentum changing perturbations is not accessible by Lyapunov functions obtained from energy and momentum. A blow-up construction transforms the stability problem to the analysis symmetry-breaking perturbations of Hamiltonian relative equilibria. As such, the stability follows by KAM theory rather than energy-momentum confinement.

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