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Geometric Mechanics, Lagrangian Reduction, and Nonholonomic Systems

In: Mathematics Unlimited — 2001 and Beyond

Author

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  • Hernán Cendra
  • Jerrold E. Marsden
  • Tudor S. Ratiu

Abstract

This paper outlines some features of general reduction theory as well as the geometry of nonholonomic mechanical systems. In addition to this survey nature, there are some new results. Our previous work on the geometric theory of Lagrangian reduction provides a convenient context that is herein generalized to nonholonomic systems with symmetry. This provides an intrinsic geometric setting for many of the results that were previously understood primarily in coordinates. This solidification and extension of the basic theory should have several interesting consequences, some of which are spelled out in the final section of the paper. Two important references for this work are Cendra, Marsden and Ratiu [2000], hereafter denoted CMR and Bloch, Krishnaprasad, Marsden and Murray [1996], hereafter denoted BKMM.

Suggested Citation

  • Hernán Cendra & Jerrold E. Marsden & Tudor S. Ratiu, 2001. "Geometric Mechanics, Lagrangian Reduction, and Nonholonomic Systems," Springer Books, in: Björn Engquist & Wilfried Schmid (ed.), Mathematics Unlimited — 2001 and Beyond, pages 221-273, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56478-9_10
    DOI: 10.1007/978-3-642-56478-9_10
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