超细长弹性杆的Noether对称性及守恒量  

Noether Symmetries and the Conserved Quantities for Super-long Elastic Slender Rod

作　　者：翁玉权[1] 

机构地区：[1]青岛大学数学科学学院,山东青岛266071

出　　处：《青岛大学学报（自然科学版）》2008年第1期36-39,共4页Journal of Qingdao University(Natural Science Edition)

摘　　要：基于Kirchhoff的动力学比拟技巧将动力学中的时间变量t置换为弧长变量s,研究圆截面弹性杆在欧拉角坐标下的Hamilton函数,并给出了标准Hamilton方程形式,利用与动力学相似的方法给出Noether对称变换的定义和拟广义Killing非线形微分方程组,以及由Noether对称变换导出的Noether守恒量定理并给出了该定理的数学逻辑证明,最后利用守恒定理求解出具体的守恒量的计算实例。This paper focuses on the Noether symmetries and the conserved quantities of a super-long elastic slender rod, an important structural model of DNA and other long-train molecules. Based on Kirchhoff＇s analogue, generalized Hamilton canonical equations are analyzed. The Noether transformations and the Noether theorem are introduced. The Noether symmetries and conserved quantities of the model are presented by using the infinitesimal transformations.

关 键 词：Kirchhoff比拟 Noether对称变换 Killing方程 守衡量 

分 类 号：O302[理学—力学]