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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：99 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.
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.
