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