Jacobi椭圆函数有理式的Fourier级数<sup>*</sup>

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

Jacobi椭圆函数有理式的Fourier级数^*

基金项目: * 中国科学院科学基金

摘要: 本文列出了手册[1]及文献[2]中未计算过的九十余个Jacobi椭圆函数sn(u,k),cn(u,k),dn(u,k)的有理函数的Fourier展式.对于用Melnikov方法研究可积系统在周期扰动下的次谐波分枝与浑沌性质,及其他工程物理中的计算问题,这些公式可供查阅应用.

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.

[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.