10.1186/2251-7456-6-31

φ-Lagrangian and Hamiltonian mechanics on SO(2)

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  • Esmaeil Azizpour*1,
  1. Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, 41335, IR

Published in Issue 2012-08-31

How to Cite

Azizpour, E. (2012). φ-Lagrangian and Hamiltonian mechanics on SO(2). Mathematical Sciences, 6(1). https://doi.org/10.1186/2251-7456-6-31
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Abstract

Abstract Purpose In this paper, the canonical formalism for plane rotation group SO(2) is presented. Methods The φ -Lagrangian method is applied in order to find a Lagrangian that the Euler-Lagrange equations would correspondingly coincide with the Lie equations. Results The canonical formalism for plane rotation group SO (2) is presented. The Lagrangian and Hamiltonian are explicitly constructed. Conclusions We introduce a family of Lagrange functions on the plane rotation group and verify that Euler-Lagrange and Hamilton equations associated to each of these functions must coincide with the Lie equations in the Lie transformation group.

Keywords

  • Lagrangian,
  • Hamiltonian mechanics,
  • Lie equations,
  • Euler-Lagrange equations,
  • 70H03; 70H05
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References

  1. Goldstein (1950) Addison-Wesley
  2. Paal and Virkepu (2005) Plane rotations and Hamilton-Dirac mechanics Czechoslovak 55(11) (pp. 1503-1508)
  3. Antonelli and Hrimiuc (1996) On the theory of ϕ-Lagrange manifolds with applications in biology and physics 3(3) (pp. 299-333)