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Classical mechanics on fractal curves

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Fractal analogue of Newton, Lagrange, Hamilton, and Appell’s mechanics are suggested. The fractal \(\alpha\)-velocity and \(\alpha\)-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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Correspondence to Alireza Khalili Golmankhaneh.

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S.I. : Framework of Fractals in Data Analysis: Theory and Interpretation. Guest editors: Santo Banerjee, A. Gowrisankar.

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Golmankhaneh, A.K., Welch, K., Tunç, C. et al. Classical mechanics on fractal curves. Eur. Phys. J. Spec. Top. 232, 991–999 (2023).

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