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Chin. Phys. B, 2013, Vol. 22(10): 104503    DOI: 10.1088/1674-1056/22/10/104503
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Noether symmetry and conserved quantities of the analytical dynamics of a Cosserat thin elastic rod

Wang Penga, Xue Yunb, Liu Yu-Lua
a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
b School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, China
Abstract  In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables: time t and arc coordinate s. Starting from the Lagrange equations of Cosserat rod dynamics, the criterion of Noether symmetry with Lagrange style for rod dynamics is given and the Noether conserved quantity is obtained. Not only are the conservations of generalized moment and generalized energy obtained, but also some other integrals.
Keywords:  analytical mechanics      Noether symmetry      conservation laws      Cosserat elastic rod dynamics     
Received:  15 January 2013      Published:  30 August 2013
PACS:  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
  02.20.Sv (Lie algebras of Lie groups)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11262019 and 10972143).
Corresponding Authors:  Liu Yu-Lu     E-mail:  ylliu@staff.shu.edu.cn

Cite this article: 

Wang Peng, Xue Yun, Liu Yu-Lu Noether symmetry and conserved quantities of the analytical dynamics of a Cosserat thin elastic rod 2013 Chin. Phys. B 22 104503

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