Jacobi-Maupertuis metric of Lienard type equations and Jacobi Last Multiplier

2017/06/07 by Sumanto Chanda, A. Ghose‐Choudhury, Chanda, Sumanto +4
Chemistry · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #nlin.SI

paper · pdf · doi:10.48550/arxiv.1706.02219

arxiv created 2017/06/07 · openalex publication_date 2017/06/07 · arxiv updated 2017/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a construction of the Jacobi-Maupertuis (JM) principle for an equation of the Lienard type, viz x + f(x)x² + g(x) = 0 using Jacobi's last multiplier. The JM metric allows us to reformulate the Newtonian equation of motion for a variable mass as a geodesic equation for a Riemannian metric. We illustrate the procedure with examples of Painleve-Gambier XXI, the Jacobi equation and the Henon-Heiles system.

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