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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Published in: | The European physical journal. ST, Special topics Special topics, 2023-07, Vol.232 (7), p.991-999 |
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Main Authors: | , , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 1951-6355 1951-6401 |
DOI: | 10.1140/epjs/s11734-023-00775-y |