Stability by KAM confinement of certain wild, nongeneric relative equilibria of underwater vehicles with coincident centers of mass and bouyancy

摘要

Purely rotational relative equilibria of an ellipsoidal underwater vehicleoccur at nongeneric momentum where the symplectic reduced spaces changedimension. The stability these relative equilibria under momentum changingperturbations is not accessible by Lyapunov functions obtained from energy andmomentum. A blow-up construction transforms the stability problem to theanalysis symmetry-breaking perturbations of Hamiltonian relative equilibria. Assuch, the stability follows by KAM theory rather than energy-momentumconfinement.