LAGRANGIANS FOR DISSIPATIVE NONLINEAR OSCILLATORS: THE METHOD OF JACOBI LAST MULTIPLIER

被引：70

作者：

Nucci, M. C. ^{[1
]}

Tamizhmani, K. M. ^{[2
]}

机构：

[1] Univ Perugia, Dipartimento Matemat & Informat, I-06123 Perugia, Italy

[2] Pondicherry Univ, Dept Math, Kalapet 605014, Puducherry, India

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2010年 / 17卷 / 02期

关键词：

Ordinary differential equations; Lie symmetry algebra; Lagrangian; COMPLETE SYMMETRY GROUP; LIE SYMMETRIES; DIFFERENTIAL-EQUATIONS; VARIABLE-COEFFICIENTS; DYNAMICAL-SYSTEM; OLD METHOD;

D O I：

10.1142/S1402925110000696

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：167 / 178

页数：12

共 39 条

[1] Ames W.F., 1968, Nonlinear Ordinary differential equations in Transport Processes
[2] [Anonymous], NUOVO CIMENTO B
[3] [Anonymous], 1886, VORLESUNGEN DYNAMIK
[4] [Anonymous], 1844, J REINE ANGEW MATH
[5] Bianchi L., 1918, Lezioni sulla teoria dei gruppi continui finiti di trasformazioni
[6] Solution and asymptotic/blow-up behaviour of a class of nonlinear dissipative systems
Bluman, George
Cheviakov, Alexei E.
Senthilvelan, M.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 339 (02) : 1199 - 1209
[7] Lagrangian formalism for nonlinear second-order Riccati systems:: One-dimensional integrability and two-dimensional superintegrability -: art. no. 062703
Cariñena, JF
Rañada, MF
Santander, M
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2005, 46 (06)
[8] A quantum exactly solvable non-linear oscillator with quasi-harmonic behaviour
Carinena, Jose F.
Ranada, Manuel F.
Santander, Mariano
[J]. ANNALS OF PHYSICS, 2007, 322 (02) : 434 - 459
[9] Dirac P. A. M., 1933, PHYS Z SOWJETUNION, V3, P64
[10] EULER L, 1769, E366 I CALCALI INTEG

← 1 2 3 4 →