Relative equilibria for two rigid bodies connected by a ball-in-socket joint

For simple mechanical systems with symmetry, a variational principle on configuration space determines relative equilibria. This principle of symmetric criticality is applied to a problem of coupled rigid bodies. Numerical optimization by CONSOLE (a package intended originally for optimization-based control system design) is shown to be an effective technique for searching for some of the relative equilibria. A key geometric condition appears as a consequence of the variational formulation