Nonholonomic stability aspects of piecewise holonomic systems (Q1289585)

It is known that Hamiltonian systems cannot have exponentially stable steady motions. Exponential stability for some of the variables (i.e. some eigenvalues of the linearized system having negative real parts, while the others have zero real parts) becomes possible in the presence of non-holonomic constraints. Non-holonomic mechanical systems can often be linked to a ``sister system'' which is piecewise holonomic and exhibits collisional contacts resulting in energy dissipation. An example is a rimless spoked wheel replacing a rolling disk. Here the author investigates the question whether the source of exponential stability is the above dissipation or it can be attributed to the non-holonomic nature of intermittent contact. He argues by way of the example of Chaplygin sleigh that the latter can be the case.