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Lagrange formalism for particles moving in a space of fractal dimension

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Abstract

Analogs of the Lagrange equation for particles evolving in a space of fractal dimension are obtained. Two cases are considered: 1) when the space is formed by a set of material points (a so-called fractal continuum), and 2) when the space is a true fractal. In the latter case the fractional integrodifferential formalism is utilized, and a new principle for devising a fractal theory, viz., a generalized principle of least action, is proposed and used to obtain the corresponding Lagrange equation. The Lagrangians for a free particle and a closed system of interacting particles moving in a fractal continuum are derived.

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Authors and Affiliations

  1. Institute of Pulse Processes and Technologies, Ukrainian National Academy of Sciences, 327018, Nikolaev, Ukraine

    I. P. Guk

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  1. I. P. Guk
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Zh. Tekh. Fiz. 68, 7–11 (February 1990)

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Guk, I.P. Lagrange formalism for particles moving in a space of fractal dimension. Tech. Phys. 43, 353–357 (1998). https://doi.org/10.1134/1.1258985

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  • DOI: https://doi.org/10.1134/1.1258985

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