A New Minimum Principle for Lagrangian Mechanics (Articolo in rivista)

Type
Label
  • A New Minimum Principle for Lagrangian Mechanics (Articolo in rivista) (literal)
Anno
  • 2013-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1007/s00332-012-9148-z (literal)
Alternative label
  • Matthias Liero; Ulisse Stefanelli (2013)
    A New Minimum Principle for Lagrangian Mechanics
    in Journal of nonlinear science; SPRINGER, 233 SPRING ST, NEW YORK, NY 10013 (Stati Uniti d'America)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Matthias Liero; Ulisse Stefanelli (literal)
Pagina inizio
  • 179 (literal)
Pagina fine
  • 204 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://link.springer.com/article/10.1007/s00332-012-9148-z/fulltext.html (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 23 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 2 (literal)
Note
  • ISI Web of Science (WOS) (literal)
  • Scopu (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, 10117 Berlin, Germany; Istituto di Matematica Applicata e Tecnologie Informatiche \"E. Magenes\"-CNR, v. Ferrata 1, 27100 Pavia, Italy (literal)
Titolo
  • A New Minimum Principle for Lagrangian Mechanics (literal)
Abstract
  • We present a novel variational view at Lagrangian mechanics based on the minimization of weighted inertia-energy functionals on trajectories. In particular, we introduce a family of parameter-dependent global-in-time minimization problems whose respective minimizers converge to solutions of the system of Lagrange's equations. The interest in this approach is that of reformulating Lagrangian dynamics as a (class of) minimization problem(s) plus a limiting procedure. The theory may be extended in order to include dissipative effects thus providing a unified framework for both dissipative and nondissipative situations. In particular, it allows for a rigorous connection between these two regimes by means of I\"-convergence. Moreover, the variational principle may serve as a selection criterion in case of nonuniqueness of solutions. Finally, this variational approach can be localized on a finite time-horizon resulting in some sharper convergence statements and can be combined with time-discretization. (literal)
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