Summary
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Einstein A.,Ann. Phys. (Leipzig),17 (1905) 891.
Pauli W.,Theory of Relativity (Pergamon) 1958.
Hill E. L.,Phys. Rev.,72 (1947) 143.
Rohrlich F.,Ann. Phys. (N.Y.),22 (1963) 169;Classical Charged Particles (Addison-Wesley) 1965.
Rindler W.,Phys. Rev.,119 (1960) 2082.
Kichenassamy S.,C. R. Acad. Sci. Paris,260 (1965) 3001.
Bower J. W.,Contributions to the Calculus of Variations for Years 1983–1937 (University of Chicago).
Bliss G. A.,Am. J. Math.,52 (1930) 673;
Bliss G. A.,Lectures on the Calculus of Variations (University of Chicago Press) 1946.
Ewing G. M.,Calculus of Variations with Applications (W. W. Norton) 1969; subsequent reprint by Dover, 1985.
Young L. C,Lectures on the Calculus of Variations and Optimal Control Theory (N. B. Saunders) 1969; subsequent reprint by Chelsea, 1980.
Caratheodory C.,Calculus of Variations and Partial Differential Equations of the First Order (Chelsea) 1982.
Barut A. O.,Electrodynamics and Classical Theory of Fields and Particles (MacMillan) 1964; subsequent reprint by Dover, 1980.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Krikorian, R.A. On a variational formulation of uniformly accelerated motion in special relativity. Nuov Cim B 111, 723–729 (1996). https://doi.org/10.1007/BF02743402
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02743402