Jacobi-Maupertuis metric of Liénard type equations and Jacobi last multiplier

Sumanto Chanda; Anindya Ghose-Choudhury; Partha Guha

Jacobi-Maupertuis metric of Liénard type equations and Jacobi last multiplier

Sumanto Chanda, Anindya Ghose-Choudhury, Partha Guha

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We present a construction of the Jacobi-Maupertuis (JM) principle for an equation of the Liénard type, (Formula presented) 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.

Original language	British English
Article number	120
Journal	Electronic Journal of Differential Equations
Volume	2018
State	Published - 15 Jun 2018

Keywords

Jacobi's last multiplier
Jacobi-Maupertuis metric
Position-dependent mass

Cite this

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title = "Jacobi-Maupertuis metric of Li{\'e}nard type equations and Jacobi last multiplier",

abstract = "We present a construction of the Jacobi-Maupertuis (JM) principle for an equation of the Li{\'e}nard type, (Formula presented) 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 Painlev{\'e}-Gambier XXI, the Jacobi equation and the Henon-Heiles system.",

keywords = "Jacobi's last multiplier, Jacobi-Maupertuis metric, Position-dependent mass",

author = "Sumanto Chanda and Anindya Ghose-Choudhury and Partha Guha",

note = "Funding Information: Acknowledgement. We are grateful to Professor Jaume Llibre for his valuable comments. The research of PG is supported by FAPESP through Instituto de Fisica de S{\~a}o Carlos, Universidade de Sao Paulo with grant number 2016/06560-6. Publisher Copyright: {\textcopyright} 2018 Texas State University.",

year = "2018",

month = jun,

day = "15",

language = "British English",

volume = "2018",

journal = "Electronic Journal of Differential Equations",

issn = "1072-6691",

publisher = "Texas State University - San Marcos",

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T1 - Jacobi-Maupertuis metric of Liénard type equations and Jacobi last multiplier

AU - Chanda, Sumanto

AU - Ghose-Choudhury, Anindya

AU - Guha, Partha

N1 - Funding Information: Acknowledgement. We are grateful to Professor Jaume Llibre for his valuable comments. The research of PG is supported by FAPESP through Instituto de Fisica de São Carlos, Universidade de Sao Paulo with grant number 2016/06560-6. Publisher Copyright: © 2018 Texas State University.

PY - 2018/6/15

Y1 - 2018/6/15

N2 - We present a construction of the Jacobi-Maupertuis (JM) principle for an equation of the Liénard type, (Formula presented) 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.

AB - We present a construction of the Jacobi-Maupertuis (JM) principle for an equation of the Liénard type, (Formula presented) 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.

KW - Jacobi's last multiplier

KW - Jacobi-Maupertuis metric

KW - Position-dependent mass

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M3 - Article

AN - SCOPUS:85049589703

SN - 1072-6691

VL - 2018

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

M1 - 120

ER -

Jacobi-Maupertuis metric of Liénard type equations and Jacobi last multiplier

Abstract

Keywords

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