分形固体动力学
Dynamics of Fractal Solids
摘要：
我们用一种特殊的连续介质模型来描述分形固体。我们建议用分数连续模型来描述分形固体，其中所有的特征和场都在体积中的任何地方定义，但它们遵循一些由分数阶积分导出的广义方程。分数积分的阶数可以等于固体的分形质量维数。分数次积分被认为是积分在分形上的一种近似。提出了计算分形固体转动惯量的方法。分形固体的动力学由通常的欧拉方程描述。考虑了分形固体连续介质模型可能的实验检验。
英文摘要：
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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