Lagrangians for dissipative nonlinear oscillators: the method of Jacobi Last Multiplier

Details Lagrangians for dissipative nonlinear oscillators: the method of Jacobi Last Multiplier Lagrangians for dissipative nonlinear oscillators: the method of Jacobi Last Multiplier

2008-08-29

arxiv.org/abs/0809.0022v1

Physics

Mathematical Physics

13 pages

Scientific paper

We present a method devised by Jacobi to derive Lagrangians of any second-order differential equation: it consists in finding a Jacobi Last Multiplier. We illustrate the easiness and the power of Jacobi's method by applying it to several equations and also a class of equations studied by Musielak with his own method [Musielak ZE, Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients. J. Phys. A: Math. Theor. 41 (2008) 055205 (17pp)], and in particular to a Li\`enard type nonlinear oscillator, and a second-order Riccati equation.

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