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Reduction of invariant constrained systems using anholonomic frames

Michael Crampin (UGent) and Tom Mestdag (UGent)
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Abstract
We analyze two reduction methods for nonholonomic systems that are invariant under the action of a Lie group on the configuration space. Our approach for obtaining the reduced equations is entirely based on the observation that the dynamics can be represented by a second-order differential equations vector field and that in both cases the reduced dynamics can be described by expressing that vector field in terms of an appropriately chosen anholonomic frame.
Keywords
MECHANICAL SYSTEMS, NONHOLONOMIC SYSTEMS, SYMMETRY, EQUATIONS, GEOMETRY

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Citation

Please use this url to cite or link to this publication:

Chicago
Crampin, Michael, and Tom Mestdag. 2011. “Reduction of Invariant Constrained Systems Using Anholonomic Frames.” Journal of Geometric Mechanics 3 (1): 23–40.
APA
Crampin, Michael, & Mestdag, T. (2011). Reduction of invariant constrained systems using anholonomic frames. JOURNAL OF GEOMETRIC MECHANICS, 3(1), 23–40.
Vancouver
1.
Crampin M, Mestdag T. Reduction of invariant constrained systems using anholonomic frames. JOURNAL OF GEOMETRIC MECHANICS. 2011;3(1):23–40.
MLA
Crampin, Michael, and Tom Mestdag. “Reduction of Invariant Constrained Systems Using Anholonomic Frames.” JOURNAL OF GEOMETRIC MECHANICS 3.1 (2011): 23–40. Print.
@article{1860311,
  abstract     = {We analyze two reduction methods for nonholonomic systems that are invariant under the action of a Lie group on the configuration space. Our approach for obtaining the reduced equations is entirely based on the observation that the dynamics can be represented by a second-order differential equations vector field and that in both cases the reduced dynamics can be described by expressing that vector field in terms of an appropriately chosen anholonomic frame.},
  author       = {Crampin, Michael and Mestdag, Tom},
  issn         = {1941-4889},
  journal      = {JOURNAL OF GEOMETRIC MECHANICS},
  keywords     = {MECHANICAL SYSTEMS,NONHOLONOMIC SYSTEMS,SYMMETRY,EQUATIONS,GEOMETRY},
  language     = {eng},
  number       = {1},
  pages        = {23--40},
  title        = {Reduction of invariant constrained systems using anholonomic frames},
  url          = {http://dx.doi.org/10.3934/jgm.2011.3.23},
  volume       = {3},
  year         = {2011},
}

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