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

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.

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Zhang, W. (2000). Study of Central Configurations and Relative Equilibria in the Problem of Four Bodies. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Zhang, Wei. "Study of Central Configurations and Relative Equilibria in the Problem of Four Bodies." Electronic Thesis or Dissertation. University of Cincinnati, 2000. OhioLINK Electronic Theses and Dissertations Center. 30 Aug 2015.

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Zhang, Wei "Study of Central Configurations and Relative Equilibria in the Problem of Four Bodies." Electronic Thesis or Dissertation. University of Cincinnati, 2000. https://etd.ohiolink.edu/

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