http://www.cnr.it/ontology/cnr/individuo/prodotto/ID279489
A New Minimum Principle for Lagrangian Mechanics (Articolo in rivista)
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- Label
- A New Minimum Principle for Lagrangian Mechanics (Articolo in rivista) (literal)
- Anno
- 2013-01-01T00:00:00+01:00 (literal)
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- 10.1007/s00332-012-9148-z (literal)
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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)
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- Matthias Liero; Ulisse Stefanelli (literal)
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- http://link.springer.com/article/10.1007/s00332-012-9148-z/fulltext.html (literal)
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- 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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