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Lagrange equations of nonholonomic systems with fractional derivatives 被引量：7

Lagrange equations of nonholonomic systems with fractional derivatives
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摘要 This paper obtains Lagrange equations of nonholonomic systems with fractional derivatives. First, the exchanging relationships between the isochronous variation and the fractional derivatives are derived. Secondly, based on these exchanging relationships, the Hamilton＇s principle is presented for non-conservative systems with fractional derivatives. Thirdly, Lagrange equations of the systems are obtained. Furthermore, the d＇Alembert-Lagrange principle with fractional derivatives is presented, and the Lagrange equations of nonholonomic systems with fractional derivatives are studied. An example is designed to illustrate these results. This paper obtains Lagrange equations of nonholonomic systems with fractional derivatives. First, the exchanging relationships between the isochronous variation and the fractional derivatives are derived. Secondly, based on these exchanging relationships, the Hamilton＇s principle is presented for non-conservative systems with fractional derivatives. Thirdly, Lagrange equations of the systems are obtained. Furthermore, the d＇Alembert-Lagrange principle with fractional derivatives is presented, and the Lagrange equations of nonholonomic systems with fractional derivatives are studied. An example is designed to illustrate these results.
作者 周莎 傅景礼 刘咏松
机构地区 Institute of Mathematical Physics
出处 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第12期25-29,共5页 中国物理B（英文版）
基金 Project supported by the National Natural Science Foundation of China (Grant Nos. 11072218 and 10672143)
关键词 fractional derivative d＇Alembert-Lagrange principle Lagrange equation nonholonomic system fractional derivative, d＇Alembert-Lagrange principle, Lagrange equation, nonholonomic system
分类号 O316 [理学—一般力学与力学基础] O37 [理学—流体力学]
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参考文献12

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同被引文献92

  • 1FU JingLi1,LI XiaoWei2,LI ChaoRong1,ZHAO WeiJia3 & CHEN BenYong4 1 Institute of Mathematical Physics,Zhejiang Sci-Tech University,Hangzhou 310018,China,2 Department of Physics,Shangqiu Normal University,Shangqiu 476000,China,3 Department of Mathematics,Qingdao University,Qingdao 266071,China,4 Faculty of Mechanical Engineering & Automation,Zhejiang Sci-Tech University,Hangzhou 310018,China.Symmetries and exact solutions of discrete nonconservative systems[J].Science China(Physics,Mechanics & Astronomy),2010,53(9):1699-1706. 被引量：3
  • 2FU 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.Noether-type theorem for discrete nonconservative dynamical systems with nonregular lattices[J].Science China(Physics,Mechanics & Astronomy),2010,53(3):545-554. 被引量：11
  • 3刘端.NOETHER’S THEOREM AND ITS INVERSE OF NONHOLONOMIC NONCONSERVATIVE DYNAMICAL SYSTEMS[J].Science China Mathematics,1991,34(4):419-429. 被引量：17
  • 4郭柏灵,蒲学科,黄凤辉.分数阶偏微分方程及其数值解[M].北京:科学出版社,2011.
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  • 6Podlubny Igor. Fractional Differential Equations[M]. San Diego: Academic Press, 1999.
  • 7Riewe F. Nonconservative Lagrangian and Hamihonian mechanics[J]. Physical Review E, 1996, 53(2): 1890-1899.
  • 8Riewe F. Mechanics with fractional derivatioves[J]. Physical Review E, 1997, 55(3): 3581-3592.
  • 9Agrawal O P. Formulation of Euler-Lagrange equations for fractional variational problems [J]. Journal of Mathematical Analysis and Applications, 2002, 272: 368-379.
  • 10Agrawal O P. Fractional variational calculus in terms of Riesz fractional derivatives [J]. Journal of Physics A: Mathematical and Theoretical, 2007, 40: 6287-6303.

引证文献7

二级引证文献38

Chinese Physics B
2010年 第12期

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