Lagrangian Dynamics And Possible Isochronous Behavior In Several Classes Of Non-Linear Second Order Oscillators Via The Use Of Jacobi Last Multiplier

Keywords

Conservation laws; Isochronous dynamics; Isotonic potentials; Jacobi Last Multiplier (JLM); Lagrangians; Simple harmonic oscillator

Abstract

Abstract In this paper, we employ the technique of Jacobi Last Multiplier (JLM) to derive Lagrangians for several important and topical classes of non-linear second-order oscillators, including systems with variable and parametric dissipation, a generalized anharmonic oscillator, and a generalized Lane-Emden equation. For several of these systems, it is very difficult to obtain the Lagrangians directly, i.e., by solving the inverse problem of matching the Euler-Lagrange equations to the actual oscillator equation. In order to facilitate the derivation of exact solutions, and also investigate possible isochronous behavior in the analyzed systems, we next invoke some recent theoretical results and attempt to map the potential term to either the simple harmonic oscillator or the isotonic potential for specific values of the coefficient parameters of each non-linear oscillator. We find non-trivial parameter sets corresponding to isochronous dynamics in some of the considered systems, but none in others. Finally, the Lagrangians obtained here are coupled to Noether's theorem, leading to non-trivial conservation laws for several of the oscillators.

Publication Date

4-20-2015

Publication Title

International Journal of Non-Linear Mechanics

Volume

74

Number of Pages

100-107

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.ijnonlinmec.2015.04.006

Socpus ID

84929501213 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84929501213

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