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Nucci, M. C.; Tamizhmani, K. M.

Lagrangians for dissipative nonlinear oscillators: the method of Jacobi last multiplier. (English) Zbl 1206.34013

J. Nonlinear Math. Phys. 17, No. 2, 167-178 (2010).
Authors’ abstract: 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 Z. E. Musielak with his own method [J. Phys. A, Math. Theor. 41, No. 5, 055205 (2008; Zbl 1136.37044)], and in particular a Liènard type nonlinear oscillator and a second-order Riccati equation. Also, we derive more than one Lagrangian for each equation.
Reviewer: Alexey Remizov (Trieste)

Cited in 43 Documents

MSC:

34A26 Geometric methods in ordinary differential equations
34C14 Symmetries, invariants of ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms

Keywords:

second-order ordinary differential equations; Euler-Lagrange equation; Lagrangian; Lie symmetry algebra

Citations:

Zbl 1136.37044
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Full Text: DOI arXiv

References:

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