Chin. Phys. B, 2014, Vol. 23(11): 110201    DOI: 10.1088/1674-1056/23/11/110201
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# 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
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.
Keywords:  Lie symmetry      conserved quantity      fractional nonholonomic systems
Received:  11 March 2014      Revised:  11 July 2014      Accepted manuscript online:
 PACS: 02.20.-a (Group theory) 45.20.Jj (Lagrangian and Hamiltonian mechanics) 45.10.Hj (Perturbation and fractional calculus methods) 02.30.Xx (Calculus of variations)
Fund: 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).
Corresponding Authors:  Fu Jing-Li     E-mail:  sqfujingli@163.com