Reduction of Almost Poisson brackets and Hamiltonization of the Chaplygin Sphere
Symplectic Geometry
2013-06-20 v1
Abstract
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
Cite
@article{arxiv.0808.0854,
title = {Reduction of Almost Poisson brackets and Hamiltonization of the Chaplygin Sphere},
author = {Luis C. Garcia-Naranjo},
journal= {arXiv preprint arXiv:0808.0854},
year = {2013}
}