A comparison of vakonomic and nonholonomic dynamics with applications to non-invariant Chaplygin systems

24 Sep 2018  ·  Jóźwikowski Michał, Respondek Witold ·

We study relations between vakonomically and nonholonomically constrained Lagrangian dynamics for the same set of linear constraints. The basic idea is to compare both situations at the level of variational principles, not equations of motion as has been done so far... The method seems to be quite powerful and effective. In particular, it allows to derive, interpret and generalize many known results on non-Abelian Chaplygin systems. We apply it also to a class of systems on Lie groups with a left-invariant constraints distribution. Concrete examples of the unicycle in a potential field, the two-wheeled carriage and the generalized Heisenberg system are discussed. read more

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Differential Geometry Mathematical Physics Mathematical Physics