This paper develops the approach to special relativity put forward by John S. Bell. The classical dynamics of an electron orbiting a nucleus in uniform motion is solved analytically and compared to numerical simulations for an accelerated nucleus. The relativistic phenomena of length contraction and time dilation are shown to result from the electric and magnetic forces on the electron when its motion is analyzed in a single frame of reference. The relevance of these results for understanding the theory of special relativity is discussed.

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See the supplementary material online the for MATLAB code (used to produce Figs. 3 and 4) as well as details of the implementation of the numerical method described in Appendix B.
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Supplementary Material

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