1307.2387 (Robert McLachlan et al.)

Collective Lie--Poisson integrators on $\R^{3}$    [PDF]

Robert McLachlan, Klas Modin, Olivier Verdier

We develop Lie--Poisson integrators for general Hamiltonian systems on $\R^{3}$ equipped with the rigid body bracket. The method uses symplectic realisation of $\R^{3}$ on $T^{*}\R^{2}$ and application of symplectic Runge--Kutta schemes. As a side product, we obtain simple symplectic integrators for general Hamiltonian systems on the sphere $S^{2}$.

View original: http://arxiv.org/abs/1307.2387