Noether-type theorem for discrete nonconservative dynamical systems with nonregular lattices  

作　　者：FU JingLi1, CHEN LiQun2 & CHEN BenYong3 1 Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China 2 Department of Mechanics, Shanghai University, Shanghai 200072, China 3 Faculty of Mechanical-Engineering & Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China 

出　　处：《Science China(Physics,Mechanics & Astronomy)》2010年第3期545-554,共10页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 10672143 and 60575055)

摘　　要：We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices. The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems. Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the nonconserved forces under the infinitesimal transformations with respect to the time and generalized coordinates, we give the discrete analog of generalized variational formula. From this formula we derive the discrete analog of generalized Noether-type identity, and then we present the generalized quasi-extremal equations and properties of these equations for the systems. We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems. We discuss an example to illustrate these results.We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices. The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems. Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the nonconserved forces under the infinitesimal transformations with respect to the time and generalized coordinates, we give the discrete analog of generalized variational formula. From this formula we derive the discrete analog of generalized Noether-type identity, and then we present the generalized quasi-extremal equations and properties of these equations for the systems. We also obtain the discrete analog of Noether-type conserved laws and the discrete analog of generalized Noether theorems for the systems. We discuss an example to illustrate these results.

关 键 词：NOETHER symmetry VARIATIONAL formula quasi-extremal equation conservation law DISCRETE nonconserved dynamical system 

分 类 号：O302[理学—力学]