Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics

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

中国物理B ›› 2012, Vol. 21 ›› Issue (7): 70203-070203.doi: 10.1088/1674-1056/21/7/070203

Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics

王鹏^{a b}, 薛纭^c, 刘宇陆^a

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

收稿日期:2012-01-11 修回日期:2012-01-29 出版日期:2012-06-01 发布日期:2012-06-01
基金资助:
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.

Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics

Wang Peng(王鹏)^{a) b)}, Xue Yun(薛纭)^c), and Liu Yu-Lu(刘宇陆)^a)†

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

Received:2012-01-11 Revised:2012-01-29 Online:2012-06-01 Published:2012-06-01
Contact: Liu Yu-Lu E-mail:ylliu@staff.shu.edu.cn
Supported by:
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.

摘要/Abstract

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 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.

关键词: analytical mechanics, Mei symmetry, conservation laws, elastic rod

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.

Key words: analytical mechanics, Mei symmetry, conservation laws, elastic rod

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

11.30.-j (Symmetry and conservation laws) 02.30.Ik (Integrable systems) 87.14.gk (DNA)

王鹏, 薛纭, 刘宇陆 . Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics[J]. 中国物理B, 2012, 21(7): 70203-070203.

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[J]. Chin. Phys. B, 2012, 21(7): 70203-070203.

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Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics

Mei symmetry and conserved quantities in Kirchhoff thin elastic rod statics

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