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Lagrangian theory for presymplectic systems
TLDR
An algorithm is developed which solves simultaneously the problem of the compatibility of the equations of motion, the consistency of their solutions and the SODE problem and gives all the lagrangian constraints, which are completed and improved.
Hamiltonian Systems in Multisymplectic Field Theories
We consider Hamiltonian systems in first-order multisymplectic field theories. First we review the construction and properties of Hamiltonian systems in the so-called restricted multimomentum bundle…
Multivector Fields and Connections. Applications to field theories
Hamiltonian systems with constraints: a geometric approach
Hamilton-Dirac equations for a constrained Hamiltonian system are deduced from a variational principle. In the local problem for such systems an algorithm is proposed to obtain the final constraint…
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Constraint algorithm for singular field theories
It is well known that for systems of ODE’s describing singular dynamical systems, the existence and uniqueness of solutions are not assured. In many of these cases, there are geometrical constraint…
Skinner-Rusk formalism for optimal control
In 1983, the dynamics of a mechanical system was represented by a first-order system on a suitable phase space by R. Skinner and R. Rusk. The corresponding unified formalism developed for optimal…
1 2 6 A pr 2 00 6 GEOMETRIC HAMILTON – JACOBI THEORY
The Hamilton–Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in…
Geometrical Setting of Time-Dependent Regular Systems:. Alternative Models.
We analyse exhaustively the geometric formulations of the time-dependent regular dynamical systems, both the Hamiltonian and the Lagrangian formalisms. We study the equivalence between the different…
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A pr 2 01 6 Structural aspects of Hamilton – Jacobi theory
In our previous papers [11, 13] we showed that the Hamilton–Jacobi problem can be regarded as a way to describe a given dynamics on a phase space manifold in terms of a family of dynamics on a…
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