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- Title
JACOBI-MAUPERTUIS METRIC OF LIÉNARD TYPE EQUATIONS AND JACOBI LAST MULTIPLIER.
- Authors
CHANDA, SUMANTO; GHOSE-CHOUDHURY, ANINDYA; GUHA, PARTHA
- Abstract
We present a construction of the Jacobi-Maupertuis (JM) principle for an equation of the Liénard type, 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 Painlevé-Gambier XXI, the Jacobi equation and the Henon-Heiles system.
- Subjects
RIEMANNIAN metric; JACOBI'S condition; GEODESIC equation; PAINLEVE equations; EQUATIONS of motion
- Publication
Electronic Journal of Differential Equations, 2018, Vol 2018, Issue 101-157, p1
- ISSN
1550-6150
- Publication type
Article