Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constrained Dynamics: Generalized Lie Symmetries, Singular Lagrangians,
  and the Passage to Hamiltonian Mechanics   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 determined. Importantly, while second-order,
Lagrangian vector fields are not such a solution, it is always possible to
construct from them a SOELVF that is. We find that all SOELVFs are projectable
to the Hamiltonian phase space, as are all the dynamical structures in the
Lagrangian phase space needed for their evolution. In particular, the primary
Hamiltonian constraints can be constructed from vectors that lie in the kernel
of the Lagrangian two-form, and with this construction, we show that the
Lagrangian constraint algorithm for the SOELVF is equivalent to the stability
analysis of the total Hamiltonian. Importantly, the end result of this
stability analysis gives a Hamiltonian vector field that is the projection of
the SOELVF obtained from the Lagrangian constraint algorithm. The Lagrangian
and Hamiltonian formulations of mechanics for singular Lagrangians are in this
way equivalent.

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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat