牛顿力学中的Cosserat-Zhilin系统
Systems of Cosserat--Zhilin in Newtonian Mechanics
摘要：
本文在向量微积分的新概念--滑块和旋量（双测度）的基础上，引入Cosserat-Zhilin力学系统作为牛顿（非相对论）力学的主要对象。在Stocks定理适用的情况下，导出了不同类型Cosserat-Zhilin系统的运动微分方程。本文定义乘法组代表的措施，应力作为一个（定义良好）的线性各向同性映射的{应变}张量或张量的{应变速度}的经典和极性连续的2-和3-维的情况下。
英文摘要：
Mechanical systems of Cosserat--Zhilin are introduced as the main object of Newtonian (non--relativistic) mechanics on the base of new notions of vector calculus - sliders and screw measures (bi-measures). The differential equations of motion are derived for different types of Cosserat--Zhilin systems in the case where Stocks theorem is applicable. The paper defines multiplicative groups which represent the measure of stress as a (well-defined) linear isotropic map of {strain} tensor or tensor of {strain velocities} for classical and polar continua in 2- and 3-dimensional cases.
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