Lie symmetry theorem of fractional nonholonomic systems

doi:10.1088/1674-1056/23/11/110201

›› 2014, Vol. 23 ›› Issue (11): 110201-110201.doi: 10.1088/1674-1056/23/11/110201

• GENERAL • 下一篇

Lie symmetry theorem of fractional nonholonomic systems

孙毅^a, 陈本永^a, 傅景礼^b

a Faculty of Mechanical-Engineering & Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China;
b Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China

收稿日期:2014-03-11 修回日期:2014-07-11 出版日期:2014-11-15 发布日期:2014-11-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11272287 and 11472247) and the Program for Changjiang Scholars and Innovative Research Team in University of China (Grant No. IRT13097).

Lie symmetry theorem of fractional nonholonomic systems

Sun Yi (孙毅)^a, Chen Ben-Yong (陈本永)^a, Fu Jing-Li (傅景礼)^b

a Faculty of Mechanical-Engineering & Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China;
b Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China

Received:2014-03-11 Revised:2014-07-11 Online:2014-11-15 Published:2014-11-15
Contact: Fu Jing-Li E-mail:sqfujingli@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11272287 and 11472247) and the Program for Changjiang Scholars and Innovative Research Team in University of China (Grant No. IRT13097).

摘要/Abstract

摘要： The Lie symmetry theorem of fractional nonholonomic systems in terms of combined fractional derivatives is established, and the fractional Lagrange equations are obtained by virtue of the d'Alembert-Lagrange principle with fractional derivatives. As the Lie symmetry theorem is based on the invariance of differential equations under infinitesimal transformations, by introducing the differential operator of infinitesimal generators, the determining equations are obtained. Furthermore, the limit equations, the additional restriction equations, the structural equations, and the conserved quantity of Lie symmetry are acquired. An example is presented to illustrate the application of results.

关键词: Lie symmetry, conserved quantity, fractional nonholonomic systems

Abstract: The Lie symmetry theorem of fractional nonholonomic systems in terms of combined fractional derivatives is established, and the fractional Lagrange equations are obtained by virtue of the d'Alembert-Lagrange principle with fractional derivatives. As the Lie symmetry theorem is based on the invariance of differential equations under infinitesimal transformations, by introducing the differential operator of infinitesimal generators, the determining equations are obtained. Furthermore, the limit equations, the additional restriction equations, the structural equations, and the conserved quantity of Lie symmetry are acquired. An example is presented to illustrate the application of results.

Key words: Lie symmetry, conserved quantity, fractional nonholonomic systems

中图分类号: (Group theory)

02.20.-a

45.20.Jj (Lagrangian and Hamiltonian mechanics) 45.10.Hj (Perturbation and fractional calculus methods) 02.30.Xx (Calculus of variations)

孙毅, 陈本永, 傅景礼. Lie symmetry theorem of fractional nonholonomic systems[J]. , 2014, 23(11): 110201-110201.

Sun Yi (孙毅), Chen Ben-Yong (陈本永), Fu Jing-Li (傅景礼). Lie symmetry theorem of fractional nonholonomic systems[J]. Chin. Phys. B, 2014, 23(11): 110201-110201.

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Lie symmetry theorem of fractional nonholonomic systems

Lie symmetry theorem of fractional nonholonomic systems

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