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Differential invariants of a class of Lagrangian systems with two degrees of freedom

  • We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples.

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Metadaten
Author:Yulia Bagderina, Nikolai Nikolaevich TarkhanovORCiDGND
URN:urn:nbn:de:kobv:517-opus-63129
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (2 (2013) 2)
Document Type:Preprint
Language:English
Year of Completion:2013
Publishing Institution:Universität Potsdam
Release Date:2013/02/01
Tag:Euler-Lagrange equations; equivalence; invariant
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
PACS Classification:00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.20.-a Group theory (for algebraic methods in quantum mechanics, see 03.65.Fd; for symmetries in elementary particle physics, see 11.30.-j) / 02.20.Tw Infinite-dimensional Lie groups
00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.30.-f Function theory, analysis / 02.30.Hq Ordinary differential equations
00.00.00 GENERAL / 02.00.00 Mathematical methods in physics / 02.30.-f Function theory, analysis / 02.30.Ik Integrable systems
00.00.00 GENERAL / 05.00.00 Statistical physics, thermodynamics, and nonlinear dynamical systems (see also 02.50.-r Probability theory, stochastic processes, and statistics) / 05.45.-a Nonlinear dynamics and chaos (see also section 45 Classical mechanics of discrete systems; for chaos in fluid dynamics, see 47.52.+j)
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2013
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Notes extern:RVK-Klassifikation: SI 990