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