Conservative non-holonomic mechanical systems are not Hamiltonian
in general and thus are not constrained to obey the theorems
applicable to Hamiltonion systems. In particular Hamiltonian
systems cannot have assymptotic stability and non-holonomic
systems can.
But this fact has been often missed by the non-experts. Perhaps
this is because many of the common examples of non-holonomic
systems have symmetries that preclude stability. In particular,
a system that has a reflection symmetry that corresponds to
moving backwards cannot be so stable. Such systems include
a rolling hoop, ball, or symmetric top while rolling on
a flat plane, a surface of revolution or a prismatic channel.
The Chapligin sleigh is also an example of such a system if
the center of mass is on the line normal to the skate.
Non-holonomic systems that violate this symmetry, and thus
better reveal the stability possibilities of non-holonomic
systems, include a general Chaplygin Sleigh, Monte-Hubbards
skate-board, and a bicycle.
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