簡易檢索 / 詳目顯示

回結果列表
研究生： 陳乃嘉
Nai-Chia Chen
論文名稱： 具有軸對稱與三點共線的平面五體中心構形
On Symmetric Planar Central Configurations for the 5-Body Problem with 3 Collinear Masses
指導教授： 陳國璋
Kuo-Chang Chen
口試委員:
學位類別： 博士
Doctor
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2007
畢業學年度： 95
語文別： 英文
論文頁數： 17
中文關鍵詞： 中心構形
外文關鍵詞： central configuration, relative equilibrium
相關次數： 點閱：3  下載：0 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • 關於N體問題(N大於四)，平面中心構形的個數是否有限仍是未知。我們加入兩個條件：軸對稱與具有三點共線，來研究五體平面中心構形個數的有限性。在這兩個條件的限制下，証明了這兩個條件的平面五體中心構形必須是某些形狀；我們亦証明：對任何質量的選取，平面五體中心構形的個數為有限，並且給了上界。

    This article concerns the N-body problem on the existence of non-collinear
    planar central configurations with three masses on a line. For the case N = 4,
    the nonexistence can be easily proved with the Perpendicular Bisector
    Theorem, and thus we study the case N = 5. We prove that with the
    presence of axial symmetry, such central configurations could exist only in
    certain shapes. We also give an upper bound for the number of such
    configurations for any choice of masses.

    1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 An Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3 Two Lemmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4 The Convex Case: Exclude Some Shapes . . . . . . . . . . . . . . . . . . 7 5 The Convex Case: Finiteness of Solutions . . . . . . . . . . . . . . . . . 9 5.1 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.2 BKK theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 5.3 Finiteness of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6 The Non-convex Case: Finiteness of Solutions . . . . . . . . . . . . 14 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

    [1] Bernstein, D.N.: The number of roots of a system of equations, Fun.
    Anal. Appl., 9, 183V185 (1975)
    [2] Cox, D., Little, J., O'Shea, D.: Using Algebraic Geometry, New York:
    Springer, 1998.
    [3] ElBialy, M. S.: Collision singularities in celestial mechanics. SIAM J.
    Math. Anal. 21, 1563V1593 (1990)
    [4] Hagihara,Y.: Celestial Mechanics, Vol.1, MIT press, Cambridge, 240-
    241 (1970)
    [5] Hampton, M., Moeckel, R.: Finiteness of relative equilibria of the four-
    body problem, Invent. Math. 163, 289-312 (2006)
    [6] Khovansky, A.G.: Newton polytopes and toric varieties, Functional
    Anal. Appl. 11, 289-298 (1977)
    [7] Kushnirenko, A.G.: Newton polytopes and the Bezout theorem, Func-
    tional Anal. Appl. 10, 233-235 (1976)
    [8] Li, T. Y., Li, X.: amixvol, http://www.math.msu.edu/li.
    [9] Moeckel, R.: On central con gurations, Math. Z. 205, 499-517 (1990)
    [10] Moeckel, R.: Generic niteness for Dziobeck con gurations, Trans. Am.
    Math. Soc. 353, 4673-4686 (2001)
    [11] Saari, D.G.: Manifold structure for collisions and for hyperboic-
    parabolic orbits in the N-body problem, J. Di . Eqs. 55, 300-329 (1984)
    [12] Saari, D.G.: Collision, Rings, and Other Newtonian N-body Problem
    CBMS regional conference series in mathematics, no. 104., American
    Mathematical Society, Providence, R.I. (2005)
    [13] Williams, W.L.: Permanent con guration in the problem of ve bodies,
    Trans. Amer. Math. Soc. 44, 563-579 (1938)
    [14] Wintner, A.: The Analytical Foundations of Celestial Mechanics,
    Princeton Math. Series 5, Princeton Iniversity Press, Princetion, MJ.,
    (1941)

    無法下載圖示 全文公開日期 本全文未授權公開 (校內網路)
    全文公開日期 本全文未授權公開 (校外網路)

    QR CODE