A note on stability of spacecrafts and underwater vehicles

TL;DR

This paper investigates the stability of spacecraft and underwater vehicles modeled as Hamilton-Poisson systems, constructing a coordinate chart on the symplectic leaf and deriving stability conditions for a generic equilibrium point.

Contribution

It introduces a coordinate chart on the symplectic leaf and establishes new stability conditions for equilibrium points in Hamilton-Poisson models of spacecraft and underwater vehicles.

Findings

Constructed a coordinate chart on the symplectic leaf.

Derived stability conditions for equilibrium points.

Provided a framework for analyzing stability in Hamilton-Poisson systems.

Abstract

A Hamilton-Poisson system is an approach for the motion of a spacecraft around an asteroid or for the motion of an underwater vehicle. We construct a coordinate chart on the symplectic leaf which contains a specific generic equilibrium point and we establish stability conditions for this equilibrium point.