Damped equations of Mathieu type

被引：9

作者：

Choudhury, A. Ghose ^{[1
]}

Guha, Partha ^{[2
]}

机构：

[1] Surendranath Coll, Dept Phys, Kolkata 700009, India

[2] SN Bose Natl Ctr Basic Sci, Kolkata 700098, India

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2014年 / 229卷

关键词：

Mathieu equation; First integrals; Jacobi's last multiplier; Lagrangians; Van der Pol-Mathieu equation; JACOBI LAST MULTIPLIER; PENDULUM;

D O I：

10.1016/j.amc.2013.11.106

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain the first integrals of various extensions of the Mathieu equation by exploiting the integrable time-dependent classical dynamics introduced by Bartuccelli and Gentile (2003) [6]. We also compute the Lagrangian of the Van der Pol-Mathieu equation using Jacobi's last multiplier and consider certain coupled versions of time-dependent equations of the oscillator type. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：85 / 93

页数：9

共 29 条

[1] Approximate asymptotics for a nonlinear Mathieu equation using harmonic balance based averaging [J].

Abraham, GT ;

Chatterjee, A .

NONLINEAR DYNAMICS, 2003, 31 (04) :347-365

[2] A PENDULUM THEOREM [J].

ACHESON, DJ .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1993, 443 (1917) :239-245

[3]

[Anonymous], 1990, COURSE MODERN ANAL

[4]

[Anonymous], 1844, J REINE ANGEW MATH

[5]

Arnold V.I., 2006, Ordinary Differential Equations, V58291st

[6]

Arscott FM, 1964, Periodic Differential Equations

[7] On the stability of the upside-down pendulum with damping [J].

Bartuccelli, MV ;

Gentile, G ;

Georgiou, KV .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2002, 458 (2018) :255-269

[8] On a class of integrable time-dependent dynamical systems [J].

Bartuccelli, MV ;

Gentile, G .

PHYSICS LETTERS A, 2003, 307 (5-6) :274-280

[9]

Bessa E., ARXIV10065025V1NLINC

[10] On the Jacobi Last Multiplier, integrating factors and the Lagrangian formulation of differential equations of the Painleve-Gambier classification [J].

Choudhury, A. Ghose ;

Guha, Partha ;

Khanra, Barun .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 360 (02) :651-664

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