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.
NUCCI, M.C., K. M. TAMIZHMANI (2010). Lagrangians for dissipative nonlinear oscillators: the method of Jacobi Last Multiplier. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 17(2), 167-178 [10.1142/S1402925110000696].
Lagrangians for dissipative nonlinear oscillators: the method of Jacobi Last Multiplier
NUCCI, Maria Clara;
2010
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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
