On a variational formulation of uniformly accelerated motion in special relativity
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In this paper we present a derivation of the characteristic differential equation of uniformly accelerated motion, in special relativity, from a variational principle formulated in Minkowskian velocity 4-space. Because of the constraints introduced by the theory of relativity, the variational problem is reduced to an equivalent non-parametric Lagrange problem with variable end points in a five-dimensional space. The determination of the Euler-Lagrange equations requires the use of the transversality equations.
PACS04.20 Classical general relativity
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