Inverse variational problem for nonstandard Lagrangians
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Publication:2018735
DOI10.1016/S0034-4877(14)60046-XzbMATH Open1326.49059arXiv1305.6386MaRDI QIDQ2018735
Author name not available (Why is that?)
Publication date: 25 March 2015
Published in: (Search for Journal in Brave)
Abstract: The non-standard Lagrangians (NSLs) for dissipative-like dynamical systems were introduced in an ad hoc fashion rather than being derived from the solution of the inverse problem of variational calculus. We begin with the first integral of the equation of motion and solve the associated inverse problem to obtain some of the existing results for NSLs. In addition, we provide a number of alternative Lagrangian representations. The case studies envisaged by us include (i) the usual modified Emden-type equation, (ii) Emden-type equation with dissipative term quadratic in velocity and (iii) Lokta-Volterra model. We point out that our method is quite general for applications to other physical systems.
Full work available at URL: https://arxiv.org/abs/1305.6386
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