2,560 research outputs found
Singular Lagrangians and precontact Hamiltonian Systems
In this paper we discuss singular Lagrangian systems on the framework of
contact geometry. These systems exhibit a dissipative behavior in contrast with
the symplectic scenario. We develop a constraint algorithm similar to the
presymplectic one studied by Gotay and Nester (the geometrization of the
well-known Dirac-Bergman algorithm). We also construct the Hamiltonian
counterpart and prove the equivalence with the Lagrangian side. A Dirac-Jacobi
bracket is constructed similar to the Dirac bracket
Constrained Variational Calculus for Higher Order Classical Field Theories
We develop an intrinsic geometrical setting for higher order constrained
field theories. As a main tool we use an appropriate generalization of the
classical Skinner-Rusk formalism. Some examples of application are studied, in
particular, applications to the geometrical description of optimal control
theory for partial differential equations.Comment: 25 pages; 4 diagram
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