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Exploring first integrals of homogeneous Lagrangian systems through nonlocal constants
Scomparin, Mattia
2025
Abstract
In this paper we study autonomous systems whose Lagrangian function is the combination of several homogeneous terms with respect to positions and velocities. We show that, assuming certain relations between the degrees of homogeneity of such terms, the systems considered possess (in addition to energy) a further first integral that provides information about their solutions. A new feature of these results is the use of the theory of nonlocal constants, which finds useful constants using one-parameter perturbed motions.
Publisher
EUT Edizioni Università di Trieste
Source
Mattia Scomparin, "Exploring first integrals of homogeneous Lagrangian systems through nonlocal constants" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.57 (2025)", EUT Edizioni Università di Trieste, Trieste, 2025, pp.
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International