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arXiv · 1205.5299

Relativistic Linear Restoring Force

D. Clark·J. Franklin·N. Mann
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Abstract

We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right of the relativistic expressions: dp/dt or dp/dtau . Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we introduce a form of retardation appropriate for the description of a linear (in displacement) force arising from the interaction of a pair of particles with a relativistic field. The procedure is akin to replacing Coulomb's law in E&M with a retarded form (the first correction in the full relativistic case). This retardation leads to the expected oscillation, but with amplitude growth in both its relativistic and non-relativistic incarnations.

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D. Clark, J. Franklin, N. Mann. 2012-05-23. Relativistic Linear Restoring Force. https://doi.org/10.1088/0143-0807/33/5/1041

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