A Curious Use of Extra Dimension in Classical Mechanics
Trung Phan, Anh Doan
TL;DR
This paper demonstrates how extra dimensions can simplify classical mechanics problems by showing the equivalence of a 1D inverse-quadratic potential problem to free motion in higher-dimensional spaces, providing new analytical insights.
Contribution
The paper introduces a novel approach using extra dimensions to transform and analyze classical mechanics problems more simply.
Findings
Inverse-quadratic potential in 1D is equivalent to free motion in 2D Euclidean space.
The same problem maps to free motion in 3D Minkowskian space.
Extra dimensions offer a new perspective for solving classical mechanics problems.
Abstract
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 an inverse-quadratic potential in 1D is equivalent to that of another test particle moving freely in 2D Euclidean space and 3D Minkowskian space.
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Taxonomy
TopicsExperimental and Theoretical Physics Studies · Sports Dynamics and Biomechanics · Scientific Research and Discoveries