A generalization of Chaplygin’s Reducibility Theorem

    2009, Volume 14, Number 6, pp.  635-655

    Author(s): Fernandez O. E., Mestdag T., Bloch A. M.

    In this paper we study Chaplygin’s Reducibility Theorem and extend its applicability to nonholonomic systems with symmetry described by the Hamilton–Poincare–d’Alembert equations in arbitrary degrees of freedom. As special cases we extract the extension of the Theorem to nonholonomic Chaplygin systems with nonabelian symmetry groups as well as Euler–Poincaré–Suslov systems in arbitrary degrees of freedom. In the latter case, we also extend the Hamiltonization Theorem to nonholonomic systems which do not possess an invariant measure. Lastly, we extend previous work on conditionally variational systems using the results above. We illustrate the results through various examples of well-known nonholonomic systems.
    Keywords: Hamiltonization, nonholonomic systems, reducing multiplier
    Citation: Fernandez O. E., Mestdag T., Bloch A. M., A generalization of Chaplygin’s Reducibility Theorem, Regular and Chaotic Dynamics, 2009, Volume 14, Number 6, pp. 635-655

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