A note on stability of nongeneric equilibria for an underwater vehicle

TL;DR

This paper analyzes the nonlinear Lyapunov stability of nongeneric equilibria with spin in underwater vehicles, identifying invariant submanifolds and conditions for stability despite the singular nature of these equilibria.

Contribution

It introduces a novel approach to stability analysis for nongeneric equilibria by characterizing invariant submanifolds involving sub-Casimir functions.

Findings

Identification of an invariant submanifold containing nongeneric equilibria.

Conditions for nonlinear stability on the invariant submanifold.

Extension of stability analysis to singular symplectic leaves.

Abstract

We study the Lyapunov stability of a family of nongeneric equilibria with spin for underwater vehicles with noncoincident centers. The nongeneric equilibria belong to singular symplectic leaves that are not characterized as a preimage o a regular value of the Casimir functions. We find an invariant submanifold such that the nongeneric equilibria belong to a preimage of a regular value that involves sub-Casimir functions. We obtain results for nonlinear stability on this invariant submanifold.