On the stability and integration of Hamilton-Poisson systems on so(3)*_

Abstract

We consider inhomogeneous quadratic Hamilton-Poisson systems on the Lie-Poisson space so(3)*_. There are nine such systems up to affine equivalence. We investigate the stability nature of the equilibria for each of these systems. For a subclass of systems, we find explicit expressions for the integral curves in terms of Jacobi elliptic functions.

Keywords

• hamilton-poisson system
• lie-poisson structure
• lyapunov stability
• energy-casimir method
• jacobi elliptic function