Lagrangians for Dissipative Nonlinear Oscillators: The Method of Jacobi Last Multiplier

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 Liènard type nonlinear oscillator and a second-order Riccati equation. Also, we derive more than one Lagrangian for each equation.