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.
trung.phan@yale.edu
Anh Doan
Department of Astronomy and Astrophysics, Pennsylvania State University, University Park, PA 16802, U.S.A.
dnd5@psu.edu
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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