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A Fiber Bundle Approach to the Transpositional Relations in Nonholonomic Mechanics

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Abstract

The equations of nonholonomic mechanics may be derived using a number of variational principles. This paper studies some of these principles from the contemporary geometric point of view, taking into account various bundle structures that are intrinsically present in the nonholonomic setting.

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Notes

  1. Please note that, in terms of the fictitious quantities π i called “quasicoordinates” that are employed by some authors (Ehlers et al. 2005, Greenwood 2003, Neimark and Fufaev 1972, Papastavridis 2002, etc.), the components ζ i correspond to the quantities denoted in the aforementioned literature by δπ i.

  2. Neimark and Fufaev use the operator d to represent differentiation with respect to time, not differentials.

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Acknowledgements

We would like to thank the National Science Foundation for support and the reviewers for their helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, San José State University, San José, CA, 95192, USA

    Jared M. Maruskin

  2. Department of Mathematics, The University of Michigan, Ann Arbor, MI, 48109, USA

    Anthony M. Bloch

  3. Control and Dynamical Systems, California Institute of Technology, Pasadena, CA, 91125, USA

    Jerrold E. Marsden

  4. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Dmitry V. Zenkov

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  1. Jared M. Maruskin
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  2. Anthony M. Bloch
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  4. Dmitry V. Zenkov
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Correspondence to Anthony M. Bloch.

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Communicated by P. Newton.

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Maruskin, J.M., Bloch, A.M., Marsden, J.E. et al. A Fiber Bundle Approach to the Transpositional Relations in Nonholonomic Mechanics. J Nonlinear Sci 22, 431–461 (2012). https://doi.org/10.1007/s00332-012-9144-3

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