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Note on the Derivation of the Equation of Motion of a Charged Point-Particle from Hamilton's Principle

Abstract : An alternative derivation of the equation of motion of a charged point particle from Hamilton's principle is presented. The variational principle is restated as a Bolza problem of optimal control, the control variable u i , i = 0, …, 3, being the 4-velocity. The trajectory ( s) i and 4-velocity ū i ( s) of the particle is an optimal pair, i.e., it furnishes an extremum to the action integral. The pair ( , ū) satisfies a set of necessary conditions known as the maximum principle. Because of the path dependence of proper time s, we are concerned with a control problem with a free end point in the space of coordinates (s, x 0 , …, x 3 ). To obtain the equation of motion, the transversality condition must be satisfied at the free end point.
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Submitted on : Tuesday, April 19, 2022 - 2:46:21 PM
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R. A. Krikorian. Note on the Derivation of the Equation of Motion of a Charged Point-Particle from Hamilton's Principle. Astrophysics, 2015, 58, pp.244-249. ⟨10.1007/s10511-015-9379-4⟩. ⟨insu-03644940⟩

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