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The Cartan form for constrained Lagrangian systems and the nonholonomic Noether theorem

Michael Crampin (UGent) and Tom Mestdag (UGent)
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Abstract
This paper deals with conservation laws for mechanical systems with nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic systems and a Cartan form approach. We present what we believe to be the most general relations between symmetries and first integrals. We discuss the so-called nonholonomic Noether theorem in terms of our formalism, and we give applications to Riemannian submanifolds, to Lagrangians of mechanical type, and to the determination of quadratic first integrals.
Keywords
Noether theorem, symmetries, nonholonomic constraints, Lagrangian system, first integrals, conservation laws, GEOMETRY, SYMMETRY, REDUCTION, MECHANICS

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Chicago
Crampin, Michael, and Tom Mestdag. 2011. “The Cartan Form for Constrained Lagrangian Systems and the Nonholonomic Noether Theorem.” International Journal of Geometric Methods in Modern Physics 8 (4): 897–923.
APA
Crampin, Michael, & Mestdag, T. (2011). The Cartan form for constrained Lagrangian systems and the nonholonomic Noether theorem. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 8(4), 897–923.
Vancouver
1.
Crampin M, Mestdag T. The Cartan form for constrained Lagrangian systems and the nonholonomic Noether theorem. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS. 2011;8(4):897–923.
MLA
Crampin, Michael, and Tom Mestdag. “The Cartan Form for Constrained Lagrangian Systems and the Nonholonomic Noether Theorem.” INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS 8.4 (2011): 897–923. Print.
@article{1870773,
  abstract     = {This paper deals with conservation laws for mechanical systems with nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic systems and a Cartan form approach. We present what we believe to be the most general relations between symmetries and first integrals. We discuss the so-called nonholonomic Noether theorem in terms of our formalism, and we give applications to Riemannian submanifolds, to Lagrangians of mechanical type, and to the determination of quadratic first integrals.},
  author       = {Crampin, Michael and Mestdag, Tom},
  issn         = {0219-8878},
  journal      = {INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS},
  keyword      = {Noether theorem,symmetries,nonholonomic constraints,Lagrangian system,first integrals,conservation laws,GEOMETRY,SYMMETRY,REDUCTION,MECHANICS},
  language     = {eng},
  number       = {4},
  pages        = {897--923},
  title        = {The Cartan form for constrained Lagrangian systems and the nonholonomic Noether theorem},
  url          = {http://dx.doi.org/10.1142/S0219887811005452},
  volume       = {8},
  year         = {2011},
}

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