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Unified formalism for non-autonomous mechanical systems
Barbero Liñán, María; Echeverría Enríquez, Arturo; Martín de Diego, David; Muñoz Lecanda, Miguel Carlos; Román Roy, Narciso
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions
We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.
Lagrangian functions
Symplectic manifolds
Hamiltonian systems
Lagrangian and Hamiltonian formalisms
Autonomous mechanics
Symplectic and presymplectic manifolds
Lagrange, Funcions de
Hamilton, Sistemes de
Classificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
Classificació AMS::55 Algebraic topology::55R Fiber spaces and bundles
Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics
Attribution-NonCommercial-NoDerivs 2.5 Spain
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
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