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首页> 外文期刊>Journal of nonlinear mathematical physics >LAGRANGIANS FOR DISSIPATIVE NONLINEAROSCILLATORS: THE METHOD OFJACOBI LAST MULTIPLIER
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LAGRANGIANS FOR DISSIPATIVE NONLINEAROSCILLATORS: THE METHOD OFJACOBI LAST MULTIPLIER

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摘要

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, including a class of equations recently studied by Musielak with his own method Z. E. Musielak, Standard and non-standard Lagrangians for dissipative dynamical systems with variable coefficients J. Phys. A: Math. Theor. 41 (2008) 055205, and in particular a Lienard type nonlinear oscillator and a second-order Riccati equation. Also, we derive more than one Lagrangian for each equation.

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