重建极性连续统理论的基本定律和原理(Ⅹ)——主均衡定律  

Renewal of Basic Laws and Principles for Polar Continuum Theories(Ⅹ)—Master Balance Law

作　　者：戴天民[1] 

机构地区：[1]辽宁大学数学系和数学应用中心,沈阳110036

出　　处：《应用数学和力学》2006年第2期151-158,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(1007202410472041)

摘　　要：通过对诸主均衡定律和应用Noether定理得出的守恒定律进行比较,自然地导出微极连续统力学的1个统一的主均衡定律和6个物理上可能的均衡方程.其中,通过扩展众所周知和惯用的能量动量张量的概念,得到相当一般的定名为能量_动量的、能量_角动量的和能量_能量的守恒定律和均衡方程.显然,在这后3种情况下的主均衡定律中,物理场量是难以凭借直觉假定出来的.最后,作为特殊情形,直接推演出若干现有的结果.Through a comparison between the expressions of master balance laws and the conservation laws derived by the use of Noether＇ s thorem a unified master balance law and six physically possible balance equations for micropolar continuum mechanics are naturally deduced. Among them, by extending the well-known conventional concept of energy-momentum tensor, the rather general conservation laws and balance equations named after energy-momentum, energy-angular momentum and energy-energy are obtained. It is clear that the forms of the physical field quantifies in the master balance law for the last three cases could not be assumed directly perceived through the intuition. Finally, some existing results are reduced immediately as special cases.

关 键 词：统一的主均衡定律 物理场量 守恒定律 能量-动量 能量-角动量 能量-能量 

分 类 号：O33[理学—一般力学与力学基础]