Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics  

作　　者：王鹏 薛纭 刘宇陆 

机构地区：[1]Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University [2]College of Physics and Electronic Engineering,Xinjiang Normal University [3]School of Mechanical Engineering,Shanghai Institute of Technology

出　　处：《Chinese Physics B》2012年第7期26-31,共6页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant No. 10972143);the Research Plan of Higher Education Institutions of Xinjiang Autonomous Region, China (Grand No. XJEDU2010S31);the Foundation for Key Subject of Theory Physics of Xinjiang Autonomous Region, China

摘　　要：We investigate the application of the Mei symmetry analysis in finding conserved quantities for the thin elastic rod statics. By using the Mei symmetry analysis, we have obtained the Jacobi integral and the cyclic integrals for a thin elastic rod with intrinsic twisting for both the cases of circular and non-circular cross sections. Our results can be easily reduced to the results without the intrinsic twisting that have been reported. Through calculation, we find that the Noether symmetry can be more directly and easily used than the Mei symmetry in finding the first integrals for the thin elastic rod. These first integrals will be helpful in the study of exact solutions and stability, as well as the numerical simulation of the elastic rod model for DNA.We investigate the application of the Mei symmetry analysis in finding conserved quantities for the thin elastic rod statics. By using the Mei symmetry analysis, we have obtained the Jacobi integral and the cyclic integrals for a thin elastic rod with intrinsic twisting for both the cases of circular and non-circular cross sections. Our results can be easily reduced to the results without the intrinsic twisting that have been reported. Through calculation, we find that the Noether symmetry can be more directly and easily used than the Mei symmetry in finding the first integrals for the thin elastic rod. These first integrals will be helpful in the study of exact solutions and stability, as well as the numerical simulation of the elastic rod model for DNA.

关 键 词：analytical mechanics Mei symmetry conservation laws elastic rod 

分 类 号：O316[理学—一般力学与力学基础] O343[理学—力学]