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Study of Central Configurations and Relative Equilibria in the Problem of Four Bodies

Zhang, Wei
http://rave.ohiolink.edu/etdc/view?acc_num=ucin974472331

Abstract Details

2000, MS, University of Cincinnati, Engineering : Computer Science.
Central configurations and relative equilibria problems in N-body system have been studied for more than two hundred years. Due to its complexity, so far there is no complete theoretical solution when N>3. In this study, we reviewed the bifurcation study in four body system. With the help of Mathematica software package, we studied the general potential equation under the condition that the moment of inertia remains constant. By further applying symmetrical constraint and center of mass constraint, we were able to study the bifurcation appeared in four body system graphically and have a better understand about its mechanism. Meanwhile, we developed software package Minalysis with Microsoft MFC. Minalysis provides a graphical user interface (GUI) so that the user can easily perform a search for central configurations and obtain numerical results. In Minalysis, we implemented downhill simplex minimization algorithm in searching for planar central configurations. The study shows that the results of Mathematica study and numerical study match well and downhill simplex minimization algorithm is effective in central configuration and relative equilibria study, especially with the combination of GUI technique.
Dieter Schmidt (Advisor)
81 p.
Computer Science
Central configuration; relative equilibria; bifurcation; numerical analysis; downhill simplex algorithm; minimization

Recommended Citations

Citations

  • Zhang, W. (2000). Study of Central Configurations and Relative Equilibria in the Problem of Four Bodies [Master's thesis, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin974472331

    APA Style (7th edition)

  • Zhang, Wei. Study of Central Configurations and Relative Equilibria in the Problem of Four Bodies. 2000. University of Cincinnati, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin974472331.

    MLA Style (8th edition)

  • Zhang, Wei. "Study of Central Configurations and Relative Equilibria in the Problem of Four Bodies." Master's thesis, University of Cincinnati, 2000. http://rave.ohiolink.edu/etdc/view?acc_num=ucin974472331

    Chicago Manual of Style (17th edition)

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This open access ETD is published by University of Cincinnati and OhioLINK.