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Advances in the Theory of Control, Signals and Systems with Physical Modeling pp 141–152Cite as

Nonholonomic Mechanics, Dissipation and Quantization

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 407))

Abstract

In this review paper we consider some of the basics of nonholonomic systems, considering in particular how it is possible do derive nonholonomic equations of motion as a limit of a Lagrangian system subject to dissipation. This in then extended to show how dissipation may be induced from a Hamiltonian field with a view to quantization of the system.

Support from NSF grants DMS-0604307 and DMS-0907949 is gratefully acknowledged.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109

    Anthony M. Bloch

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  1. Anthony M. Bloch
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Editor information

Editors and Affiliations

  1. CAS, Unité Mathématiques et Systémes, MINES-ParisTech, 35, rue Saint-Honoré, 77300, Fontainebleau, France

    Jean Lévine

  2. Laboratoire d’ Automatique, Faculté des Sciences de l’Ingénieur Station 9, CH-1015, Lausanne, Switzerland

    Philippe Müllhaupt

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Bloch, A.M. (2010). Nonholonomic Mechanics, Dissipation and Quantization. In: Lévine, J., Müllhaupt, P. (eds) Advances in the Theory of Control, Signals and Systems with Physical Modeling. Lecture Notes in Control and Information Sciences, vol 407. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16135-3_12

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  • DOI: https://doi.org/10.1007/978-3-642-16135-3_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16134-6

  • Online ISBN: 978-3-642-16135-3

  • eBook Packages: EngineeringEngineering (R0)

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