Runge-Kutta Collocation Methods for Rigid Body Lie-Poisson Equations

T. Ergenc, B. Karasozen

The author thanks P. Rentrop for his very warm hospitality at the Department of Mathematics, Technische Hochschule Darmstadt

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.

C.R. CATEGORIES : G.1.7

KEYWORDS: Lie-Poisson system, one-forms, Euler top, Runge-Kutta methods