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Hamiltonization of nonholonomic systems and the inverse problem of the calculus of variations

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Abstract
We introduce a method which allows one to recover the equations of motion of a class of nonholonomic systems by finding instead an unconstrained Hamiltonian system on the full phase space, and to restrict the resulting canonical equations to an appropriate submanifold of phase space. We focus first on the Lagrangian picture of the method and deduce the corresponding Hamiltonian from the Legendre transformation. We illustrate the method with several examples and we discuss its relationship to the Pontryagin maximum principle.

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MLA
Bloch, Anthony M., Oscar E. Fernandez, and Tom Mestdag. “Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations.” Reports on Mathematical Physics 63.2 (2009): 225–249. Print.
APA
Bloch, A. M., Fernandez, O. E., & Mestdag, T. (2009). Hamiltonization of nonholonomic systems and the inverse problem of the calculus of variations. Reports on Mathematical Physics, 63(2), 225–249.
Chicago author-date
Bloch, Anthony M., Oscar E. Fernandez, and Tom Mestdag. 2009. “Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations.” Reports on Mathematical Physics 63 (2): 225–249.
Chicago author-date (all authors)
Bloch, Anthony M., Oscar E. Fernandez, and Tom Mestdag. 2009. “Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations.” Reports on Mathematical Physics 63 (2): 225–249.
Vancouver
1.
Bloch AM, Fernandez OE, Mestdag T. Hamiltonization of nonholonomic systems and the inverse problem of the calculus of variations. Reports on Mathematical Physics. Elsevier Ltd.; 2009;63(2):225–49.
IEEE
[1]
A. M. Bloch, O. E. Fernandez, and T. Mestdag, “Hamiltonization of nonholonomic systems and the inverse problem of the calculus of variations,” Reports on Mathematical Physics, vol. 63, no. 2, pp. 225–249, 2009.
@article{714621,
  abstract     = {We introduce a method which allows one to recover the equations of motion of a class of nonholonomic systems by finding instead an unconstrained Hamiltonian system on the full phase space, and to restrict the resulting canonical equations to an appropriate submanifold of phase space. We focus first on the Lagrangian picture of the method and deduce the corresponding Hamiltonian from the Legendre transformation. We illustrate the method with several examples and we discuss its relationship to the Pontryagin maximum principle.},
  author       = {Bloch, Anthony M. and Fernandez, Oscar E. and Mestdag, Tom},
  issn         = {0034-4877},
  journal      = {Reports on Mathematical Physics},
  language     = {eng},
  number       = {2},
  pages        = {225--249},
  publisher    = {Elsevier Ltd.},
  title        = {Hamiltonization of nonholonomic systems and the inverse problem of the calculus of variations},
  url          = {http://dx.doi.org/10.1016/S0034-4877(09)90001-5},
  volume       = {63},
  year         = {2009},
}

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