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Journal for Geometry and Graphics 25 (2021), No. 2, 265--270
Copyright Heldermann Verlag 2021

A Curious Use of Extra Dimension in Classical Mechanics: Geometrization of Potential

Trung V. Phan
Department of Molecular, Cellular, and Developmental Biology, Yale University, New Haven, CT 06520, U.S.A.

Anh Doan
Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802, U.S.A.

Extra dimensions can be utilized to simplify problems in classical mechanics, offering new insights. Here we show a simple example of how the motion of a test particle under the influence of a 1D inverse-quadratic potential is equivalent to that of another test particle moving freely in 2D Euclidean space and 3D Minkowskian space.

Keywords: Particle motion, inverse-quadratic potential, Minkowskian space.

MSC: 70B05; 97M50.

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