We derive an explicit second order reversible Poisson integrator for
symmetric rigid bodies in space (i.e. without a fixed point). The integrator
is obtained by applying a splitting method to the Hamiltonian
after reduction by the S1 body symmetry. In the particular case of a
magnetic top in an axisymmetric magnetic field (i.e. the Levitron) this
integrator preserves the two momentum integrals. The method is used
to calculate the complicated boundary of stability near a linearly stable
relative equilibrium of the Levitron with indefinite Hamiltonian.
This pre-print has been submitted, and accepted, to the journal, Regular and chaotic dynamics. The definitive version: DULLIN, H.R., 2004. Poisson integrator for symmetric rigid bodies. Regular and chaotic dynamics, 9(3), pp.255-264.