Stability of equilibrium states in the Zhukovski case of heavy gyrostat using algebraic methods

TL;DR

This paper investigates the stability of equilibrium states in a heavy gyrostat's Zhukovski case using algebraic methods to construct Lyapunov functions from conserved quantities.

Contribution

It introduces an algebraic approach to analyze stability by constructing Lyapunov functions based on conserved quantities for the heavy gyrostat system.

Findings

Identified conditions for stability of equilibrium points

Developed a method to construct Lyapunov functions algebraically

Applied the method successfully to the Zhukovski case

Abstract

We study the stability of the equilibrium points of a skew product system. We analyze the possibility to construct a Lyapunov function using a set of conserved quantities and solving an algebraic system. We apply the theoretical results to study the stability of an equilibrium state of a heavy gyrostat in the Zhukovski case.