Jacobi-Maupertuis metric of Lienard type equations and Jacobi last multiplier
Date
2018-06-15
Authors
Chanda, Sumanto
Ghose-Choudhury, Anindya
Guha, Partha
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We present a construction of the Jacobi-Maupertuis (JM) principle for an equation of the Liénard type,
ẍ + ƒ(x)ẋ2 + 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 Painlevé-Gambier XXI, the Jacobi equation and the Henon-Heiles system.
Description
Keywords
Jacobi-Maupertuis metric, Position-dependent mass, Jacobi's last multiplier
Citation
Chanda, S., Ghose-Choudhury, A., & Guha, P. (2018). Jacobi-Maupertuis metric of Lienard type equations and Jacobi last multiplier. <i>Electronic Journal of Differential Equations, 2018</i>(120), pp. 1-9.
Rights
Attribution 4.0 International