Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices

doi:10.1088/1674-1056/21/7/070202

中国物理B ›› 2012, Vol. 21 ›› Issue (7): 70202-070202.doi: 10.1088/1674-1056/21/7/070202

Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices

夏丽莉^{a b}, 陈立群^{a 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

收稿日期:2011-11-30 修回日期:2011-12-28 出版日期:2012-06-01 发布日期:2012-06-01
基金资助:
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).

Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices

Xia Li-Li(夏丽莉)^a)b) and Chen Li-Qun(陈立群)^a)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

Received:2011-11-30 Revised:2011-12-28 Online:2012-06-01 Published:2012-06-01
Contact: Chen Li-Qun E-mail:lqchen@staff.shu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: discrete nonholonomic Hamiltonian systems, Lie point symmetry, Noether conserved quantity

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.

Key words: discrete nonholonomic Hamiltonian systems, Lie point symmetry, Noether conserved quantity

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

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)

夏丽莉, 陈立群. Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices[J]. 中国物理B, 2012, 21(7): 70202-070202.

Xia Li-Li(夏丽莉) and Chen Li-Qun(陈立群) . Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices[J]. Chin. Phys. B, 2012, 21(7): 70202-070202.

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Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices

Noether conserved quantities and Lie point symmetries for difference nonholonomic Hamiltonian systems in irregular lattices

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