Lagrangians for dissipative nonlinear oscillators: the method of Jacobi Last Multiplier

2008/08/29 by M. C. Nucci, K. M. Tamizhmani, Nucci, M. C. +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0809.0022

openalex publication_date 2008/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a method devised by Jacobi to derive Lagrangians of any second-order differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness and the power of Jacobi's method by applying it to several equations and also a class of equations studied by Musielak with his own method [Musielak ZE, Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients. J. Phys. A: Math. Theor. 41 (2008) 055205 (17pp)], and in particular to a Liènard type nonlinear oscillator, and a second-order Riccati equation.

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