虚物质导数与局部变分——张量变分学的基本概念及其定义  

VIRTUAL PARTICLE TIME DERIVATIVE AND LOCAL VARIATIONAL——BASIC CONCEPTS IN TENSOR VARIATIONAL THEORY

作　　者：殷雅俊[1] YIN Yajun(Department of Engineering Mechanics,School of Aerospace,Tsinghua University,Beijing 100084,China)

机构地区：[1]清华大学航天航空学院工程力学系,北京100084

出　　处：《力学与实践》2020年第6期681-688,共8页Mechanics in Engineering

基　　金：国家自然科学基金资助项目(11672150,11272175)。

摘　　要：张量分析学存在对称性破缺现象:既存在概念上的对称性破缺——有张量微分,但没有张量变分;又存在理论上的对称性破缺——有张量微分学,但没有张量变分学。然而,近年来的研究进展表明,破缺的对称性是可以弥补的。本文将综述弥补过程:回顾虚物质导数概念的拓展历史,再现张量局部变分概念的抽象过程,展示张量变分学的构建历程,揭示张量变分学与张量微分学之间的对称性。In the tensor analysis,symmetry breakages exist in concepts—there is differential of tensor,but there is no variational of tensor;in theories—there is differential theory of tensor,but there is no variational theory of tensor.However,the symmetry breakages can be compensated,as shown in this paper.The developing history of the concept of the virtual particle time derivative will be reviewed,as well as the process of abstracting the concept of the local variational of tensor and the procedure of constructing the variational theory of tensor.The symmetry between the variational theory and the differential theory for tensor will thus be revealed.

关 键 词：虚物质导数 局部变分 张量微分学 张量变分学 

分 类 号：O183[理学—数学]