Date Approved

5-5-1997

Embargo Period

8-24-2016

Document Type

Thesis

Degree Name

M.A. in Mathematics Education

Department

Science, Technology, Engineering, Arts and Math Education

College

College of Education

Advisor

Sooy, John

Subject(s)

Many-body problem--Numerical solutions; Many-body problem--Study and teaching (Higher)

Disciplines

Science and Mathematics Education

Abstract

The purpose of the study is to investigate simple solutions of the many-body problem otherwise known as the n-body problem. The study focuses on elementary solutions of the n-body problem that can be understood by undergraduate students and college preparatory students of applied. mathematics.

Historical origins of the problems were traced to the ancient Egyptians, Babylonians, and Greeks. Further development and interest dated back to the time of Copernicus, Galileo, Kepler, and finally to Newton who proposed its modern form.

Analytical and numerical solutions of specific n-body problems were solved to demonstrate solvability of certain types of n-body problems. Analytical solutions for velocities of the masses were calculated. Numerical methods written in the QB computer language generate solutions of specific n-body problems. Two- and three-body numerical solutions were solved to demonstrate solvability by writing a computer algorithm using the Euler or Runge-Kutta method. The numerical solution displays the trajectories of the masses in graphics and the behavior the masses are shown. No formula has been developed for determining general solutions of n-body problems in this research.

In conclusion, there are simple solutions for certain n-body problems. The subject can be studied at the undergraduate and college preparatory Level.

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