Dynamics of 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.

12 pages, LaTeX

References in corpus (10)

• Continuous Medium Model for Fractal Media
• Fractional Ginzburg-Landau equation for fractal media
• Fractional Hydrodynamic Equations for Fractal Media
• Fractional Generalization of Liouville Equations
• Fractional Systems and Fractional Bogoliubov Hierarchy Equations
• Fractional Liouville and BBGKI Equations
• Fractional Fokker-Planck Equation for Fractal Media
• Electromagnetic field of fractal distribution of charged particles
• Wave Equation for Fractal Solid String
• Possible Experimental Test of Continuous Medium Model for Fractal Media

Cited by in corpus (11)

• Continuous Limit of Discrete Systems with Long-Range Interaction
• Vector Calculus in Non-Integer Dimensional Space and its Applications to Fractal Media
• Anisotropic Fractal Media by Vector Calculus in Non-Integer Dimensional Space
• Non-Standard Extensions of Gradient Elasticity: Fractional Non-Locality, Memory and Fractality
• Map of Discrete System into Continuous
• Fractional Derivative as Fractional Power of Derivative
• Flow of Fractal Fluid in Pipes: Non-Integer Dimensional Space Approach
• Elasticity of Fractal Material by Continuum Model with Non-Integer Dimensional Space
• Saturn rings: fractal structure and random field model
• Application of Geometric measure Theory in Continuum Mechanics: The Configuration Space, Principle of Virtual Power and Cauchy's Stress Theory for Rough Bodies
• The configuration space and principle of virtual work for rough bodies