Abstract
We shall start with a short review of the prerelativistic mechanics of Newton, Lagrange, and Hamilton. For simplicity we restrict ourselves to systems of a single-point particle having (constant) mass m > 0. Let the parameterized motion curve be given by xα = X α(t), in the Euclidean space E3. Let the three components of the force vector be given by f α(t, x, v), which are functions of seven real variables. Here t stands for the time variable, x = (x1,x2, x3) are the spatial coordinates in a Cartesian coordinate system, and v = (v1, v2, v3) are the velocity variables.
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References
P. G. Bergman, Introduction to the Theory of Relativity, Prentice-Hall, New Jersey, 1942. [pp. 134, 158]
P. A. M. Dirac, Canad. J. Math. 2 (1950), 129–148.
I. M. Gelfand and S. V. Fomin, Calculus of variations, Prentice-Hall, New Jersey, 1963. [p. 128]
C. Lanczos, The variational principles of mechanics, University of Toronto Press, Toronto, 1977. [pp. 126, 128, 131, 134, 136, 137]
J. L. Synge, Relativity: The special theory, North-Holland, Amsterdam, 1964. [pp. 141, 145, 147, 150]
—, Classical dynamics, Reprint from Handbuch der Physik, Springer-Verlag, Berlin, 1960. [p. 157]
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© 1993 Springer Science+Business Media New York
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Das, A. (1993). The Special Relativistic Mechanics. In: The Special Theory of Relativity. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0893-8_5
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DOI: https://doi.org/10.1007/978-1-4612-0893-8_5
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