2024-03-29T00:07:45Zhttp://digital.csic.es/dspace-oai/requestoai:digital.csic.es:10261/41652021-05-20T18:09:01Zcom_10261_27com_10261_4col_10261_280
Unified formalism for non-autonomous mechanical systems
Barbero-Liñán, María
Echeverría-Enríquez, Arturo
Martin de Diego, David
Muñoz-Lecanda, Miguel C.
Roman-Roy, Narciso
Lagrangian and Hamiltonian formalisms
Autonomous mechanics
Symplectic and presymplectic manifolds
Mathematical Physics
15 pp.-- MSC classes: 37J05, 53D05, 55R10, 70H03, 70H05.
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.
We acknowledge the financial support of Ministerio de Educación y Ciencia, Projects MTM2005-04947, MTM2007-62478, and S-0505/ESP/0158 of the CAM. One of us (MBL) also acknowledges the financial support of the FPU grant AP20040096.
Peer reviewed
2008-05-12T12:24:52Z
2008-05-12T12:24:52Z
2008-03-28
preprint
http://purl.org/coar/resource_type/c_816b
arXiv:0803.4085v1 [math-ph]
http://hdl.handle.net/10261/4165
en
Preprint
open
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