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研究生： 林珈璟
Lin, Jia-Jing
論文名稱： Stability of p-elastic curves
Stability of p-elastic curves
指導教授： 林俊吉
Lin, Chun-Chi
口試委員： 崔茂培 郭庭榕 林俊吉
口試日期： 2021/07/26
學位類別： 碩士
Master
系所名稱： 數學系
Department of Mathematics
論文出版年： 2021
畢業學年度： 109
語文別： 英文
論文頁數： 17
英文關鍵詞： Stability, p-elastic curves
DOI URL： http://doi.org/10.6345/NTNU202101630
論文種類： 學術論文
相關次數： 點閱：101  下載：8 
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    • In this paper, we will discuss the stability of p-elastic curves with p ∈ (1,∞).
    We derive the first variation and second variation of p-elastic energy of curves,
    and obtain the induced Euler-Lagrange equation and stability operator, which is
    used to study the stability of equilibrium solutions.
    We mainly focus on p-elastic curves in a two dimensional plane.

    Contents 1 Introduction 1 2 Variation Formulas 1 2.1 Variation 2 2.2 First Variation formula 3 2.3 Second Variation formula 5 3 curvature of p-elastic curves 8 3.1 Normal type p-elastic curves 8 3.2 Flat-core type p-elastic curves 13 4 Stability of p-elastic curves 16 4.1 line segments 16 4.2 circles 16

    References
    [1] K. Watanabe, Planar p-elastic curves and related generalized complete elliptic integrals.
    In Kodai Math J. 37, pages 453-474, 2014.
    [2] H. Yanamoto, On the elastic closed plane curves. In Kodai Math J. 8, 224-235, 1985.
    [3] M. Giaquinta, S. Hildebrandt, Calculus of Variations I, New York, Springer, 2004.

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