TL;DR
This paper introduces a fractional continuous model to describe the dynamics of fractal solids, using fractional integrals aligned with the fractal dimension, and discusses methods to compute moments of inertia within this framework.
Contribution
It proposes a novel fractional integral-based continuous medium model for fractal solids, extending classical mechanics to fractal geometries.
Findings
Fractional integrals approximate integrals on fractals.
Euler's equations are applicable to fractal solids.
Method for computing moments of inertia in fractal solids.
Abstract
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some generalized equations which are derived by using integrals of fractional order. The order of fractional integral can be equal to the fractal mass dimension of the solid. Fractional integrals are considered as an approximation of integrals on fractals. We suggest the approach to compute the moments of inertia for fractal solids. The dynamics of fractal solids are described by the usual Euler's equations. The possible experimental test of the continuous medium model for fractal solids is considered.
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