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Georgia Journal of Science

Article Title

THE USE OF THE EULER-CROMER NUMERICAL METHOD IN CLASSICAL MECHANICS

Abstract

Because of our limited capability in obtaining analytic solutions to complicated problems, quite often, in a course on classical mechanics, the need to solve differential equations numerically arises. The majority of problems that arise in classical mechanics come from the application of Newton's 2nd law of motion. It is, therefore, important that students gain an understanding of the process involved in order to tackle solutions to second order differential equations numerically. In an effort to introduce students to such a numerical process, I incorporate the simplest numerical technique; i.e., the Euler-Cromer method. For over several decades, it has been known that the Euler-Cromer method does well in problems that involve oscillations. In my experience this is certainly true, and, while teaching a classical mechanics course, I have had a first hand opportunity to test it on several interesting examples. In most cases, analytic solutions are obtained for the simpler versions of the problems and the numerical approach is used for the complicated version. The results are compared to each other, for the cases studied, and one finds that, given the simplicity and versatility of the Euler-Cromer method, it ought to be more widely introduced in junior level physics. Additionally, I have developed a functional approach that would make it much easier for students to apply the approach in a MATLAB/Octave computational environment. The idea is simple enough that it can be easily adapted to other computational platforms.

Acknowledgements

UWG SEEP Mini-grant Program

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