Fourier Series of Rational Fractions of Jacobian Elliptic Functions

Wan Shi-dong; Li Ji-bin

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Wan Shi-dong, Li Ji-bin. Fourier Series of Rational Fractions of Jacobian Elliptic Functions[J]. Applied Mathematics and Mechanics, 1988, 9(6): 499-513.

Citation:

Wan Shi-dong, Li Ji-bin. Fourier Series of Rational Fractions of Jacobian Elliptic Functions[J]. Applied Mathematics and Mechanics, 1988, 9(6): 499-513.

Citation:

Wan Shi-dong, Li Ji-bin. Fourier Series of Rational Fractions of Jacobian Elliptic Functions[J]. Applied Mathematics and Mechanics, 1988, 9(6): 499-513.

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Fourier Series of Rational Fractions of Jacobian Elliptic Functions

Wan Shi-dong¹,
Li Ji-bin²

1.
Yunnan University, Kunming;
2.
Kunming Engineering Institute, Kunming

Received Date: 1986-11-29
Publish Date: 1988-06-15

Abstract

Abstract

In this paper more than ninety of the Fourier series of rational fractions of Jacobian elliptic functions sn(u.k), cn(u.k) and dn(u.k) are listed, which cannot be found in the, handbook and Ref. [2]. For the detection and study of chaotic behavior and subharmonic bifurcations in a two-dimensional Hamiltonian system subject to external periodic forcing by Melnikov's method, and for study of some problems of physical science and engineering, these formulas can be used.

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References(6)

References

[1]	Byrd,P.F.and M.D.Friedman,Handbook of Elliptic Integrals for Engineers and Scientists.Springer-Verlag(1971).
[2]	Langebartel,R.G.,Fourier expansions of rational fractions of elliptic integrals and Jacobian elliptic functions,SIAM,J.of Math.Anal.,11,3(1980),506-513.
[3]	Hofstadter,D.R.,奇异吸引子:在秩序与混沌之间巧妙维持平衡的数学模型,科学(中译本),3(1982),92-102
[4]	Guckenheimer,J.and P.J.Holmes,Nonlinear Oscillations,Dynamical Systems and Bifurcations of Vector Fields,Springer-Verlag(1983).
[5]	Lin Chang,Liu Zheng-rong and Li Ji-bin,Subharmonic bifurcations and chaotic behavior in system planar quadratic Hamiltonian system with periodic perturbation,Proceedings of the International Conference on Nonlinear Mechanics,Shanghai,China,October(1985),28-31.
[6]	李继彬等,三次非线性振子的次谐波分岔与浑沌性质,桂林全国非线性系统中的不稳定性与随机性会议交流资料(1984),10.