Lagrange equations of nonholonomic systems with fractional derivatives

doi:10.1088/1674-1056/19/12/120301

中国物理B ›› 2010, Vol. 19 ›› Issue (12): 120301-120301.doi: 10.1088/1674-1056/19/12/120301

Lagrange equations of nonholonomic systems with fractional derivatives

周莎, 傅景礼, 刘咏松

Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China

收稿日期:2010-07-09 修回日期:2010-07-26 出版日期:2010-12-15 发布日期:2010-12-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11072218 and 10672143).

Lagrange equations of nonholonomic systems with fractional derivatives

Zhou Sha(周莎), Fu Jing-Li(傅景礼)^†, and Liu Yong-Song(刘咏松)^‡

Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China

Received:2010-07-09 Revised:2010-07-26 Online:2010-12-15 Published:2010-12-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11072218 and 10672143).

摘要/Abstract

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.

Abstract: 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.

Key words: fractional derivative, d'Alembert–Lagrange principle, Lagrange equation, nonholonomic system

中图分类号:

0320

周莎, 傅景礼, 刘咏松. Lagrange equations of nonholonomic systems with fractional derivatives[J]. 中国物理B, 2010, 19(12): 120301-120301.

Zhou Sha(周莎), Fu Jing-Li(傅景礼), and Liu Yong-Song(刘咏松). Lagrange equations of nonholonomic systems with fractional derivatives[J]. Chin. Phys. B, 2010, 19(12): 120301-120301.

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Lagrange equations of nonholonomic systems with fractional derivatives

Lagrange equations of nonholonomic systems with fractional derivatives

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