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Abstract: We introduce a version of the Hamiltonian formalism based on the Clairautequation theory, which allows us a self-consistent description of systems withdegenerate or singular Lagrangian. A generalization of the Legendre transformto the case, when the Hessian is zero is done using the mixedenvelope-general solutions of the multidimensional Clairaut equation. Thecorresponding system of equations of motion is equivalent to the initialLagrange equations, but contains -nondynamical- momenta and unresolvedvelocities. This system is reduced to the physical phase space and presented inthe Hamiltonian form by introducing a new non-Lie bracket.



Author: Steven Duplij Center for Mathematics, Science and Education, Rutgers University and Theory Group, Nuclear Physics Labs, V. N. Kar

Source: https://arxiv.org/







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