It has been known since the early 1900's that although nonholonomic systems are not Hamiltonian,
they can nonetheless be put into a Hamiltonian form via a suitable time reparameterization (a process
called Hamiltonization). In this talk I will discuss this procedure, along with recent work extending
the basic theorem in the field (the Chaplygin Reducibility Theorem). In addition, I will discuss the
many applications that arise if a nonholonomic system is Hamiltonizable. in particular, the interesting
idea of applying variational integrators to these non-variational systems will be discussed, as will
the equally interesting but somewhat more challenging question of the quantization of a nonholonomic
system.
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