Discrete Fractional Lagrange Equations of Nonconservative Systems  

作　　者：SONG Chuanjing ZHANG Yi 

机构地区：[1]School of Mathematics and Physics,Suzhou University of Science and Technology [2]College of Civil Engineering,Suzhou University of Science and Technology

出　　处：《Transactions of Nanjing University of Aeronautics and Astronautics》2019年第1期175-180,共6页南京航空航天大学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11802193, 11572212,11272227);the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (18KJB130005);the Science Research Foundation of Suzhou University of Science and Technology(331812137);Natural Science Foundation of Suzhou University of Science and Technology

摘　　要：In order to study discrete nonconservative system,Hamilton's principle within fractional difference operators of Riemann-Liouville type is given. Discrete Lagrange equations of the nonconservative system as well as the nonconservative system with dynamic constraint are established within fractional difference operators of Riemann-Liouville type from the view of time scales. Firstly,time scale calculus and fractional calculus are reviewed.Secondly,with the help of the properties of time scale calculus,discrete Lagrange equation of the nonconservative system within fractional difference operators of Riemann-Liouville type is presented. Thirdly,using the Lagrange multipliers,discrete Lagrange equation of the nonconservative system with dynamic constraint is also established.Then two special cases are discussed. Finally,two examples are devoted to illustrate the results.In order to study discrete nonconservative system,Hamilton's principle within fractional difference operators of Riemann-Liouville type is given. Discrete Lagrange equations of the nonconservative system as well as the nonconservative system with dynamic constraint are established within fractional difference operators of Riemann-Liouville type from the view of time scales. Firstly,time scale calculus and fractional calculus are reviewed.Secondly,with the help of the properties of time scale calculus,discrete Lagrange equation of the nonconservative system within fractional difference operators of Riemann-Liouville type is presented. Thirdly,using the Lagrange multipliers,discrete Lagrange equation of the nonconservative system with dynamic constraint is also established.Then two special cases are discussed. Finally,two examples are devoted to illustrate the results.

关 键 词：DISCRETE LAGRANGE equation time scale FRACTIONAL DIFFERENCE OPERATOR NONCONSERVATIVE system 

分 类 号：O316[理学—一般力学与力学基础]