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研究生： 楊智恩
論文名稱： 超大質量雙黑洞星系中恆星軌道之研究
指導教授： 葉麗琴
口試委員:
學位類別： 碩士
Master
系所名稱： 南大校區系所調整院務中心 - 應用數學系所
應用數學系所(English)
論文出版年： 2014
畢業學年度： 102
中文關鍵詞： supermassive binary black hole 、orbits
外文關鍵詞： 超大質量雙黑洞, 軌道
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    • 摘要
    對超大質量雙黑洞星系的動態系統進行研究。此模型是由限制三體問題演變而成，其中星系位能被視為額外加入的能量。在相等質量的雙黑洞條件之下，對不同初始條件的恆星之軌道進行研究。

    Abstract
    The dynamics of galactic systems with central supermassive binary black holes is studied. The model is a modification from the restricted three body problem, in which a galactic potential is added as an external potential. Considering the case with equal mass binary black holes, the orbits of particles under the galactic potential for different initial conditions are investigated.

    Chapter 1 Introduction 1 Chapter 2 The Model 3 Chapter 3 The Equilibrium Points 9 Chapter 4 Simulation Results 12 Section 4.1 Model A: E_0=-H/3,u^2+v^2=H/3 14 Section 4.2 Model B: E_0=-7H/18,u^2+v^2=4H/18 22 Section 4.3 Model C: E_0=-8H/18,u^2+v^2=2H/18 28 Section 4.4 Model D: E_0=-17H/36,u^2+v^2=2H/36 34 Section 4.5 Model E: E_0=-([H])/2,u^2+v^2=H-[H] 40 Chapter 5 The orbit behaviors near the equilibrium points and the black hole 45 Section 5.1 near the equilibrium point L1 45 Section 5.2 near the equilibrium point L2 46 Section 5.3 near the equilibrium point L4 47 Section 5.4 near the equilibrium point JY1 48 Section 5.5 near the black hole of right hand side 49 Chapter 6 Conclusion 51 Section 6.1 Discussion Table 6.1.1. 52 Section 6.2 Summary 54 Bibliography 55 Appendix A: The initial conditions for the case E_0=-H/3 57 Appendix B: The initial conditions for the case E_0=-7H/18 58 Appendix C: The initial conditions for the case E_0=-8H/18 59 Appendix D: The initial conditions for the case E_0=-17H/36 60 Appendix E: The initial conditions for the case E_0=-([H])/2 61 Appendix F: The initial conditions for the initial location at (0,1.07) 62 Appendix G: The program 63 Appendix H: Making gif files by gnuplot 66

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