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.
%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
}