Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics

doi:10.1088/1674-1056/21/7/070203

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
Revised: 29 January 2012
Accepted manuscript online:

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(王鹏), Xue Yun(薛纭), and Liu Yu-Lu(刘宇陆) Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics 2012 Chin. Phys. B 21 070203

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Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics

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