Degenerate equilibria in mechanical systems

We consider Hamiltonian mechanical systems upon which non-holonomic, Pfaffian constraints are imposed. The critical manifold is introduced, and it is shown that the potentially stable equilibria are those points for which the Hamiltonian can be used as a local Lyapunov function. If the dynamics of the linearized system is oscillatory, but exhibits multiple eigenfrequencies of the same value, an instability occurs due to the non-holonomy of the system.