https://doi.org/10.1140/epjp/s13360-023-03695-x
Regular Article
Method of deriving Lagrangian for two-dimensional systems
1
Centre for Nonlinear Science and Engineering, Department of Physics, School of Electrical and Electronics Engineering, SASTRA Deemed University, 613401, Thanjavur, Tamil Nadu, India
2
Department of Physics, KCG College of Technology, Karapakkam, 600 097, Chennai, Tamil Nadu, India
3
Centre for Computational Modeling, Chennai Institute of Technology, 600069, Chennai, Tamil Nadu, India
4
Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, 620024, Tiruchirappalli, Tamil Nadu, India
Received:
9
November
2022
Accepted:
11
January
2023
Published online:
20
January
2023
Identifying higher dimensional nonlinear ordinary differential equations (ODEs) possessing a Lagrangian structure is a challenging problem. In this paper, we obtain a set of constraints in the form of Helmholtz conditions which are to be satisfied by a system of two coupled second-order ODEs in order to posses a Lagrangian structure. We propose a systematic algorithmic procedure to solve the underlying determining equations to obtain the Lagrangian. We demonstrate the analysis with suitable examples.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
