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- Title
A New Minimum Principle for Lagrangian Mechanics.
- Authors
Liero, Matthias; Stefanelli, Ulisse
- 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 Γ-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.
- Subjects
LAGRANGIAN mechanics; FUNCTIONALS; TRAJECTORIES (Mechanics); PROBLEM solving; STOCHASTIC convergence; PARAMETER estimation; LAGRANGE equations
- Publication
Journal of Nonlinear Science, 2013, Vol 23, Issue 2, p179
- ISSN
0938-8974
- Publication type
Article
- DOI
10.1007/s00332-012-9148-z