The Hamiltonian dynamics of the two gyrostats problem (Q1976103)

The authors discuss the problem of two gyrostats in a central force field, considering the mutual interaction between orbital and rotational motion. It is proved that the Newton-Euler equations are Hamiltonian with respect to a certain non-canonical structure. The authors show that the number of degrees of freedom can be reduced, and give an explicit form of the corresponding non-canonical Poisson bracket. In a special case when one of the gyrostats has null gyrostatic momentum, all equilibria are unstable in the zeroth-order approximation.