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Chin. Phys. B, 2012, Vol. 21(7): 070203    DOI: 10.1088/1674-1056/21/7/070203
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Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics

Wang Penga b, Xue Yunc, Liu Yu-Lua
a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
b College of Physics and Electronic Engineering, Xinjiang Normal University, Urumqi 830054, China;
c School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, China
Abstract  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 the 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 studying of exact solutions and the stability as well as the numerical simulation of the elastic rod model for DNA.
Keywords:  analytical mechanics      Mei symmetry      conservation laws      elastic rod     
Received:  11 January 2012      Published:  01 June 2012
PACS:  02.20.Sv (Lie algebras of Lie groups)  
  11.30.-j (Symmetry and conservation laws)  
  02.30.Ik (Integrable systems)  
  87.14.gk (DNA)  
Fund: 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), and the Foundation for Key Subject of Theory Physics of Xinjiang Autonomous Region, China.
Corresponding Authors:  Liu Yu-Lu     E-mail:  ylliu@staff.shu.edu.cn

Cite this article: 

Wang Peng, Xue Yun, Liu Yu-Lu Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics 2012 Chin. Phys. B 21 070203

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