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研究生: 曹祐齊
Tsao, Yu-Chi
論文名稱: 搖擺桿:建模與模擬
Swinging Sticks: Modeling and Simulation
指導教授: 陳樹杰
Chern, Shuh-Jye
口試委員: 石至文
高淑蓉
陳樹杰
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系
Department of Mathematics
論文出版年: 2013
畢業學年度: 101
語文別: 英文
論文頁數: 35
中文關鍵詞: 搖擺桿混沌平衡點單擺雙擺
外文關鍵詞: Swinging Sricks, Melnikov, pendulum
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  • 搖擺桿是一個不規則的旋轉運動系統。在這篇論文中,建立幾個搖擺
    桿的模型,並在位相空間中模擬桿子的混沌運動。


    The swinging sticks is a system with irregular rotational motions. In this thesis, several models of swinging sticks are formulated and the simulations show chaotic motions of the sticks.

    1 Introduction 1 2 Chaotic Motions of a Single Stick 2 2.1 Equation of Motion 2 2.2 Separatrix Solution 3 2.3 Melnikov's analysis 4 3 Double Sticks without Periodic Forcing 12 3.1 Equation of Motion 12 3.2 Equilibria and Stability 16 3.3 Damped Double Sticks 19 3.4 Numerical Simulation 24 4 Double Sticks-Damped with Periodic Forcing 29 4.1 Numerical Simulation 29 5 Conclusion 34 References 35

    [1] Arnold, V.I., Mathematical Methods of Classical Mechanics, Springer-Verlag, (1989).
    [2] Chetaev, N.G., The stability of Motion, Pergamon Press, (1961).
    [3] Dullin, H.R., Melnikov's method applied to the double pendulum, Z. Phys. B93, 521-528, (1994).
    [4] Hsu, S.B., Ordinary Di erential Equations with Applications, World Scienti c, (2006).
    [5] Marsdan, J.E., and Ratiu,T.S., Introduction to Mechanics and Symmetry, Springer-Verlag,
    (1999).
    [6] Perko, L., Di erential Equations and Dynamical Systems, Springer-Verlag, (1996).
    [7] Wiggins, S., Global Bifurcations and Chaos, Springer-Verlag, (1988).
    [8] Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-
    Verlag, (1990).
    [9] Zajac, E.E., The Kelvin-Tait-Chetaev theorem and extensions, J.Aeronaut. Sci 11, 46-49,
    (1964).
    3

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