# 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={Journal of Physics Communications}, year={2020}, volume={4} }

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—called second-order, Euler–Lagrange vector fields (SOELVFs)—with integral flows that have this symmetry are determined. Importantly, while…

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