Discrete Fractional Lagrange Equations of Nonconservative Systems

被引：0
|
作者：
Song C. [1 ]
Zhang Y. [2 ]
机构：
[1] School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou
[2] College of Civil Engineering, Suzhou University of Science and Technology, Suzhou
来源：
Transactions of Nanjing University of Aeronautics and Astronautics | 2019年 / 36卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Discrete Lagrange equation; Fractional difference operator; Nonconservative system; Time scale;
D O I：
10.16356/j.1005-1120.2019.01.017
中图分类号：
学科分类号：
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 RiemannLiouville 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. © 2019, Editorial Department of Transactions of NUAA. All right reserved.
引用
收藏
页码：175 / 180
页数：5
相关论文
共 50 条
  • [21] Symmetries and exact solutions of discrete nonconservative systems
    JingLi Fu
    XiaoWei Li
    ChaoRong Li
    WeiJia Zhao
    BenYong Chen
    Science China Physics, Mechanics and Astronomy, 2010, 53 : 1699 - 1706
  • [22] Symmetries and exact solutions of discrete nonconservative systems
    FU JingLi1
    2 Department of Physics
    3 Department of Mathematics
    4 Faculty of Mechanical Engineering & Automation
    Science China(Physics,Mechanics & Astronomy), 2010, Mechanics & Astronomy)2010 (09) : 1699 - 1706
  • [23] First integrals of the discrete nonconservative and nonholonomic systems
    Zhang, HB
    Chen, LQ
    Liu, RW
    CHINESE PHYSICS, 2005, 14 (02): : 238 - 243
  • [24] Fractional Euler-Lagrange equations of motion in fractional space
    Muslih, Sami I.
    Baleanu, Dumitru
    JOURNAL OF VIBRATION AND CONTROL, 2007, 13 (9-10) : 1209 - 1216
  • [25] Fractional Euler-Lagrange equations revisited
    Herzallah, Mohamed A. E.
    Baleanu, Dumitru
    NONLINEAR DYNAMICS, 2012, 69 (03) : 977 - 982
  • [26] On the Numerical Solution of Nonconservative Hyperbolic Systems of Equations
    R. R. Polekhina
    M. V. Alekseev
    E. B. Savenkov
    Differential Equations, 2023, 59 : 970 - 984
  • [27] ON THE ENERGY THEOREM FOR THE LAGRANGE EQUATIONS IN THE DISCRETE CASE
    GOTUSSO, L
    APPLIED MATHEMATICS AND COMPUTATION, 1985, 17 (02) : 129 - 136
  • [28] On the Numerical Solution of Nonconservative Hyperbolic Systems of Equations
    Polekhina, R. R.
    Alekseev, M. V.
    Savenkov, E. B.
    DIFFERENTIAL EQUATIONS, 2023, 59 (07) : 970 - 984
  • [29] Fuzzy discrete fractional calculus and fuzzy fractional discrete equations
    Hoa, Ngo Van
    Phu, Nguyen Dinh
    FUZZY SETS AND SYSTEMS, 2024, 492
  • [30] On Hamilton’s principle for discrete systems of variable mass and the corresponding Lagrange’s equations
    William C. Guttner
    Celso P. Pesce
    Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2017, 39 : 1969 - 1976
12345