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dc.contributor.author張文欣en_US
dc.contributor.authorChang, Wen-Hsinen_US
dc.contributor.author李榮耀en_US
dc.contributor.authorLee, Jong-Eaoen_US
dc.date.accessioned2014-12-12T01:57:37Z-
dc.date.available2014-12-12T01:57:37Z-
dc.date.issued2011en_US
dc.identifier.urihttp://140.113.39.130/cdrfb3/record/nctu/#GT079922520en_US
dc.identifier.urihttp://hdl.handle.net/11536/49763-
dc.description.abstractSine-Gordorn方程之某特殊解滿足二階微分方程,此為單擺運動方程式。 此論文主要探討兩部份,我們利用代數與幾何方法定義一個新曲面黎曼面替代複數平面,使得 在此黎曼面上是單值且可解析的函數。在黎曼面上對封閉曲線的基底 a,b-cycles 積分可以解決許多微分方程的問題。我們可以找到 a,b-cycles 的等價路徑,由Cauchy Integral Theorem得a,b-cycles 積分值與它們的等價路徑積分值相等。利用Mathematica,等價路徑的積分值可以被正確的求出。其次我們學習了橢圓函數並分析其性質,尤其是Weierstrass和Jacobian 這兩個代表性的橢圓函數。利用這些古典函數分析 ,求其正解及相關性質。zh_TW
dc.description.abstractThe well-known sine-Gordorn equation has certain particular solution satisfying the 2nd-order ordinary equation.In the paper we analyze the nonlinear approximation and the exact theory of the pendulum motion .In the process of solving the motion , the function occur, which are two-valued. In order to analyze it, we develop new surface to replace complex plane for such that is a single-valued function. We call the Riemann surface of genus N. With proper cut-structure, we can compute integrals of a,b-cycles and any curves on ,and analyze certain properties of. Furthermore,we study classical elliptic functions. From which , we can solve the exact solution. In terms of those functions. And we are also able to analyze certain properties of this equation.en_US
dc.language.isoen_USen_US
dc.subject單擺運動zh_TW
dc.subjectPendulum Motionsen_US
dc.title在D型代數結構下之N相黎曼空間的單擺運動之確切理論與數值運算zh_TW
dc.titleThe Exact Theory and Numerical Computations of Pendulum Motions on Riemann Surfaces of Genus N with Cut‐Structures of Type Den_US
dc.typeThesisen_US
dc.contributor.department應用數學系所zh_TW
Appears in Collections:Thesis