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

[11]

Euler L., 1769, E366 I CALCULI INTEG

[12] The Riccati and Ermakov-Pinney hierarchies [J].

Euler, Marianna ;

Euler, Norbert ;

Leach, Peter .

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2007, 14 (02) :290-310

[13]

Guha P., PREPRINT

[14]

Jacobi C G J., 1845, J. Reine Angew. Math, V29, P333

[15]

Jacobi C G J., 1845, J. Reine Angew. Math, V29, P213

[16]

Jacobi C.G.J., 1844, GIORNALE ARCADICO SC, VXCIX, P129

[17] THE ERMAKOV EQUATION: A COMMENTARY [J].

Leach, P. G. L. ;

Andriopoulos, K. .

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2008, 2 (02) :146-157

[18]

Mak M.K., ARXIV12046545V1

[19]

Mathieu E., 1868, J. Math. Pures Appl, V13, P137

[20]

McLachlan N.W., 1947, Theory and Application of Mathieu Functions

← 1 2 3 →