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Poincar\'e, the Dynamics of the Electron, and Relativity
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On June 5, 1905 Poincar\'e presented a Note to the Acad\'emie des Sciences entitled "Sur la dynamique de l'\'electron" ("On the Dynamics of the Electron"). After briefly recalling the context that led Poincar\'e to write this Note, we comment its content. We emphasize that Poincar\'e's electron model consists in assuming that the interior of the worldtube of the (hollow) electron is filled with a positive cosmological constant. We then discuss the several novel contributions to the physico-mathematical aspects of Special Relativity which are sketched in the Note, though they are downplayed by Poincar\'e who describes them as having only completed the May 1904 results of Lorentz "dans quelques points de d\'etail" ("in a few points of detail").
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Defining of three-dimensional acceleration and inertial mass leading to the simple form F=MA of relativistic motion equation
A new definition of relativistic acceleration A makes the relativistic equation of motion take the simple form F = M A with M = mγ, unifying longitudinal and transverse mass.
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