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

页码：175 / 180

页数：5

共 50 条

[1] Discrete Fractional Lagrange Equations of Nonconservative Systems
SONG Chuanjing
ZHANG Yi
TransactionsofNanjingUniversityofAeronauticsandAstronautics, 2019, 36 (01) : 175 - 180
[2] Fractional Complex Euler-Lagrange Equation: Nonconservative Systems
Toma, Antonela
Postavaru, Octavian
FRACTAL AND FRACTIONAL, 2023, 7 (11)
[3] Discrete Lagrange equations for thermofluid systems
Fahrenthold, Eric P.
Hean, Charles R.
JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME, 2008, 130 (01): : 0110091 - 0110097
[4] Lagrange equations of nonholonomic systems with fractional derivatives
周莎
傅景礼
刘咏松
Chinese Physics B, 2010, 19 (12) : 29 - 33
[5] Lagrange equations of nonholonomic systems with fractional derivatives
Zhou Sha
Fu Jing-Li
Liu Yong-Song
CHINESE PHYSICS B, 2010, 19 (12)
[6] Variational principle and dynamical equations of discrete nonconservative holonomic systems
Department of Physics, Shaoguan University, Shaoguan 512005, China
不详
Chin. Phys., 2006, 2 (249-252):
[7] Variational principle and dynamical equations of discrete nonconservative holonomic systems
Liu, RW
Zhang, HB
Chen, LQ
CHINESE PHYSICS, 2006, 15 (02): : 249 - 252
[8] Fractional Euler-Lagrange equations for constrained systems
Avkar, T
Baleanu, D
GLOBAL ANALYSIS AND APPLIED MATHEMATICS, 2004, 729 : 84 - 90
[9] DISCRETE LAGRANGE EQUATIONS
POTTS, RB
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1988, 37 (02) : 227 - 233
[10] Fractional Euler-Lagrange Equations Applied to Oscillatory Systems
David, Sergio Adriani
Valentim, Carlos Alberto, Jr.
MATHEMATICS, 2015, 3 (02): : 258 - 272

← 1 2 3 4 5 →