Runge-Kutta collocation methods for rigid body lie-poisson equations

Abstract

The rigid body Lie-Poisson structure in three dimensions is considered. We show that the symplectic collocation type Runge-Kutta methods preserve the one-form of the underlying system. The linear error growth, energy and momentum conservation properties of the numerical solutions are discussed for Euler top equation.

Keywords:

• Lie-Poisson system
• one-forms
• Euler top
• Runge-Kutta methods

C.R. Categories::

• G.1.7

^∗ The Author thsnks P.Rentrop for this very Warm hospitality at the Department of Mathe-matics,Technische Hochsule Dramstadt

^∗ The Author thsnks P.Rentrop for this very Warm hospitality at the Department of Mathe-matics,Technische Hochsule Dramstadt

Notes

^∗ The Author thsnks P.Rentrop for this very Warm hospitality at the Department of Mathe-matics,Technische Hochsule Dramstadt