弹性连续系统的Noether理论  

Noether's Theory of Elastic Continuous System

作　　者：方刚[1,2] 栾锡武 栾一功[3] FANG Gang LUAN Xiwu LUAN Yigong(The Key Laboratory of Gas Hydrate, Ministry of Land and Resources, Qingdao Institute of Marine Geology, Qingdao 266071, Shandong Province, China Laboratory for Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao 266071, Shandong Province, China School of Science, China University of Petroleum, Qingdao 266580, Shandong Province, China)

机构地区：[1]青岛海洋地质研究所,国土资源部天然气水合物重点实验室,山东青岛266071 [2]青岛海洋科学与技术国家实验室,海洋矿产资源评价与探测技术功能实验室,山东青岛266071 [3]中国石油大学(华东)理学院,山东青岛266580

出　　处：《吉林大学学报（理学版）》2017年第5期1278-1284,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:41504109);山东省自然科学基金(批准号:BS2015HZ008)

摘　　要：考虑弹性连续系统的Noether对称性与守恒量理论.先基于等参量变分和非等参量变分导出弹性连续系统Hamilton作用量变分的基本公式;再给出弹性连续系统Noether对称性的定义,得出其Noether对称性的判定条件——Noether等式,以及系统Noether对称性导致的Noether守恒量,并给出弹性连续系统的Noether定理;最后以弹性介质中传播的平面波为例给出应用.We considered the theory of Noether＇s symmetry and conserved quantity for elastic continuous system.Firstly,basic formulas for the Hamilton action variation of elastic continuous system were derived based on the equivalent and non-equivalent parameters variations.Secondly,we gave the definition of Noether＇s symmetry for elastic continuous system and obtained the determinant condition of Noether＇s symmetry：Noether＇s identity.Then we obtained the Noether＇s conserved quantity resulting from the Noether＇s symmetry of the system,and put forward the Noether＇s theorem for elastic continuous system.Finally,the example of plane wave propagating in the elastic medium was used to illustrate the application of the results.

关 键 词：弹性连续系统 NOETHER对称性 守恒量 非等参量变分 

分 类 号：O413[理学—理论物理]