Classical mechanics on fractal curves

Fractal analogue of Newton, Lagrange, Hamilton, and Appell’s mechanics are suggested. The fractal α -velocity and α -acceleration are defined in order to obtain the Langevin equation on fractal curves. Using the Legendre transformation, Hamilton’s mechanics on fractal curves is derived for modeling...

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Bibliographic Details
Published in:The European physical journal. ST, Special topics Special topics, 2023-07, Vol.232 (7), p.991-999
Main Authors: Golmankhaneh, Alireza Khalili, Welch, Kerri, Tunç, Cemil, Gasimov, Yusif S.
Format: Article
Language:English
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Summary:Fractal analogue of Newton, Lagrange, Hamilton, and Appell’s mechanics are suggested. The fractal α -velocity and α -acceleration are defined in order to obtain the Langevin equation on fractal curves. Using the Legendre transformation, Hamilton’s mechanics on fractal curves is derived for modeling a non-conservative system on fractal curves with fractional dimensions. Fractal differential equations have solutions that are non-differentiable in the sense of ordinary derivatives and explain space and time with fractional dimensions. The illustrated examples with graphs present the details.
ISSN:1951-6355
1951-6401
DOI:10.1140/epjs/s11734-023-00775-y