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March  2010, 3(1): 37-60. doi: 10.3934/dcdss.2010.3.37

Reduction of almost Poisson brackets and Hamiltonization of the Chaplygin sphere

Luis García-Naranjo 1,

1. 

Section de Mathematiques, Station 8, EPFL, CH-1015 Lausanne

Received  July 2008 Revised  December 2008 Published  December 2009

We construct different almost Poisson brackets for nonholonomic systems than those existing in the literature and study their reduction. Such brackets are built by considering non-canonical two-forms on the cotangent bundle of configuration space and then carrying out a projection onto the constraint space that encodes the Lagrange-D'Alembert principle. We justify the need for this type of brackets by working out the reduction of the celebrated Chaplygin sphere rolling problem. Our construction provides a geometric explanation of the Hamiltonization of the problem given by A. V. Borisov and I. S. Mamaev.
Keywords: Nonholonomic Systems, Chaplyigin Sphere., Hamiltonization.
Mathematics Subject Classification: Primary: 70F25; Secondary: 53D1.
Citation: Luis García-Naranjo. Reduction of almost Poisson brackets and Hamiltonization of the Chaplygin sphere. Discrete & Continuous Dynamical Systems - S, 2010, 3 (1) : 37-60. doi: 10.3934/dcdss.2010.3.37
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