臺灣博碩士論文加值系統

渾沌 ( chaos ) 是一門新興的學問。雖然它起源於非線性系統的分析，但是渾沌的觀念可以拓展延伸到生態、社會等方面而不光只是侷限在物理現象的解釋上而已。由於電腦科技的發展，使得一些原本複雜難解的系統可以由電腦加以模擬，進而帶動了渾沌現象的相關研究。
本問題是研究一經由馬達所驅動的複擺 ( double pendulum ) 之動態行為及渾沌現象。利用電腦的模擬，觀察及分析在調整三個參數 (馬達的轉速、兩個擺臂個別的長度)以及兩個擺臂的初始狀態之後，因為這些參數的改變所造成的動態行為差異。

"Chaos" is a science rising from the study of nonlinear dynamics . Its concepts can be used not only in the explanation of physical phenomenon but in biology and social science . Because of the development in computer technology , most complex systems can be simulated in computer , and this development promotes the researches about chaos .
This thesis is concerned about the phenomenon of a simple double-pendulum system driven by a motor . From the simulation in computers , we can observe and analyze the difference in dynamics as we change the three parameters and initial conditions of this system .

論文摘要……………………………………………i
英文摘要……………………………………………ii
目錄…………………………………………………iii
圖目錄………………………………………………v
符號表………………………………………………ix
第一章 渾沌簡介……………………………… 1
1-1 緒論……………………………………………1
1-2 非線性方程式的解與解的穩定性……………2
1-3 Poincare截面…………………………………6
1-4 通往渾沌的路徑……………………………6
1-5 吸引子…………………………………………8
1-6 分維及分形……………………………………9
1-7 保守系統中的渾沌現象………………………11
1-8 研究動機………………………………………16
第二章 系統方程式推導…………………………18
2-1 方程式推導……………………………………18
2-2 數值方法………………………………………20
第三章 結果及討論………………………………23
3-1 馬達轉速對系統狀態的影響…………………24
3-2 擺臂長度對系統狀態的影響…………………29
3-3 截面初始位置對系統狀態的影響……………32
3-4 角度發散率……………………………………35
第四章 結論………………………………………39
4-1 結論……………………………………………39
4-2 未來研究方向…………………………………40
參考文獻…………………………………………42
結果圖…………………………………………44

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