Constrained dynamics: generalized Lie symmetries, singular Lagrangians, and the passage to Hamiltonian mechanics

@article{Speliotopoulos2020ConstrainedDG,
  title={Constrained dynamics: generalized Lie symmetries, singular Lagrangians, and the passage to Hamiltonian mechanics},
  author={Achilles D. Speliotopoulos},
  journal={arXiv: Mathematical Physics},
  year={2020}
}
  • A. Speliotopoulos
  • Published 12 May 2020
  • Physics, Mathematics
  • arXiv: Mathematical Physics
Guided by the symmetries of the Euler-Lagrange equations of motion, a study of the constrained dynamics of singular Lagrangians is presented. We find that these equations of motion admit a generalized Lie symmetry, and on the Lagrangian phase space the generators of this symmetry lie in the kernel of the Lagrangian two-form. Solutions of the energy equation\textemdash called second-order, Euler-Lagrange vector fields (SOELVFs)\textemdash with integral flows that have this symmetry are… 

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