%0 Generic %1 balseiro2019conserved %A Balseiro, Paula %A Yapu, Luis P. %D 2019 %K differential-geometry %T Conserved quantities and Hamiltonization of nonholonomic systems %U http://arxiv.org/abs/1904.00235 %X This paper studies hamiltonization of nonholonomic systems using geometric tools. By making use of symmetries and suitable first integrals of the system, we explicitly define a global 2-form for which the gauge transformed nonholonomic bracket gives rise to a new bracket on the reduced space codifying the nonholonomic dynamics and carrying an almost symplectic foliation (determined by the common level sets of the first integrals). In appropriate coordinates, this 2-form is shown to agree with the one previously introduced locally in 34. We use our coordinate-free viewpoint to study various geometric features of the reduced brackets. We apply our formulas to obtain a new geometric proof of the hamiltonization of a homogeneous ball rolling without sliding in the interior side of a convex surface of revolution using our formulas.

@misc{balseiro2019conserved, abstract = {This paper studies hamiltonization of nonholonomic systems using geometric tools. By making use of symmetries and suitable first integrals of the system, we explicitly define a global 2-form for which the gauge transformed nonholonomic bracket gives rise to a new bracket on the reduced space codifying the nonholonomic dynamics and carrying an almost symplectic foliation (determined by the common level sets of the first integrals). In appropriate coordinates, this 2-form is shown to agree with the one previously introduced locally in [34]. We use our coordinate-free viewpoint to study various geometric features of the reduced brackets. We apply our formulas to obtain a new geometric proof of the hamiltonization of a homogeneous ball rolling without sliding in the interior side of a convex surface of revolution using our formulas.}, added-at = {2019-04-02T11:21:40.000+0200}, author = {Balseiro, Paula and Yapu, Luis P.}, biburl = {https://www.bibsonomy.org/bibtex/2a3363e32876852e7f553e54d1a18042d/dchatter}, description = {1904.00235.pdf}, interhash = {0eed969460521e6b9039886c5440111a}, intrahash = {a3363e32876852e7f553e54d1a18042d}, keywords = {differential-geometry}, note = {cite arxiv:1904.00235}, timestamp = {2019-04-02T11:21:40.000+0200}, title = {Conserved quantities and Hamiltonization of nonholonomic systems}, url = {http://arxiv.org/abs/1904.00235}, year = 2019 }