Numerical Integration of the Generalized Euler Equations

For the generalized Euler equations on arbitrary finite dimensional Lie groups explicit numerical integration schemes that preserve either the underlying Lie-Poisson structure or the Hamiltonian (energy) of the problem are derived. The concept of energy preservation is generalized to so-called M-orthogonal schemes and it is shown that certain energy preserving schemes are actually M-orthogonal. We also provide a backward error analysis for those schemes.”