| 分形力学的数学基础 |
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| 引用本文： | 谢和平. 分形力学的数学基础[J]. 力学进展, 1995, 25(2): 174-185. DOI: 10.6052/1000-0992-1995-2-J1995-024 |
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| 作者姓名： | 谢和平 |
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| 作者单位： | 中国矿业大学(北京校区)岩石力学与分行研究所 |
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| 基金项目： | 国家自然科学基金，国家科委重大基础性理论课题“非线性科学”项目和国家教委跨世纪优秀人才专项基金 |
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| 摘 要： | 在分形空间考虑的力学称为分形力学。由于分形理论的特点，分形力学的描述需要引入新的空间概念、新的数学手段和方法。本文从介绍空间、测度和维数入手，引入了分形空间，Ｂｅｓｏｖ空间和分形插值方法，进而介绍了在分形边界和分形体中力学量和力学定律的定义。
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| 关 键 词： | 分形力学 Besov空间 分形插值 |
MATHEMATICAL FOUNDATION OF FRAVTAL MECHANICS |
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| Xie Heping. MATHEMATICAL FOUNDATION OF FRAVTAL MECHANICS[J]. Advances in Mechanics, 1995, 25(2): 174-185. DOI: 10.6052/1000-0992-1995-2-J1995-024 |
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| Authors: | Xie Heping |
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| Abstract: | Mechanics based on a fractal dimension space is defined as fractal mechanics,According to fractal theory, fractal mechanics should be described hy introducing new space concepts and new mathematical tools,In this paper,space, measure and dimension are first introduced,Fractal space, Besov space and the method of fractal interpolation function are then described in details. Moreover,the definition of mechanical quantities and laws on a fractal boundary and a fractal body is discussed. |
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| Keywords: | fractal mechanics Besov space fractal interpolation |
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