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Chin. Phys. B, 2012, Vol. 21(7): 070202    DOI: 10.1088/1674-1056/21/7/070202
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Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices

Xia Li-Lia b, Chen Li-Quna c
a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China;
b Department of Physics, Henan Institute of Education, Zhengzhou 450046, China;
c Department of Mechanics, Shanghai University, Shanghai 200444, China
Abstract  The Noether conserved quantities and the Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices are studied. The generalized Hamiltonian equations of the systems are given on the basis of the transformation operators in the space of discrete Hamiltonians. The Lie transformations acting on the lattice, as well as the equations and the determining equations of the Lie symmetries are obtained for the nonholonomic Hamiltonian systems. The discrete analogue of the Noether conserved quantity is constructed by using the Lie point symmetries. An example is discussed to illustrate the results.
Keywords:  discrete nonholonomic Hamiltonian systems      Lie point symmetry      Noether conserved quantity     
Received:  30 November 2011      Published:  01 June 2012
PACS:  02.20.Sv (Lie algebras of Lie groups)  
  02.20.Qs (General properties, structure, and representation of Lie groups)  
  11.30.-j (Symmetry and conservation laws)  
  45.20.Jj (Lagrangian and Hamiltonian mechanics)  
Fund: Project supported by the National Outstanding Young Scientist Fund of China (Grant No. 10725209), the National Natural Science Foundation of China (Grant Nos. 90816001 and 11102060), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20093108110005), the Shanghai Subject Chief Scientist Project, China (Grant No. 09XD1401700), and the Shanghai Leading Academic Discipline Project, China (Grant No. S30106).
Corresponding Authors:  Chen Li-Qun     E-mail:  lqchen@staff.shu.edu.cn

Cite this article: 

Xia Li-Li, Chen Li-Qun Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices 2012 Chin. Phys. B 21 070202

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