Hamilton formalism and Noether symmetry for mechanico–electrical systems with fractional derivatives

doi:10.1088/1674-1056/21/10/100202

中国物理B ›› 2012, Vol. 21 ›› Issue (10): 100202-100202.doi: 10.1088/1674-1056/21/10/100202

Hamilton formalism and Noether symmetry for mechanico–electrical systems with fractional derivatives

张世华^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:2012-03-04 修回日期:2012-04-23 出版日期:2012-09-01 发布日期:2012-09-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11072218 and 60575055).

Hamilton formalism and Noether symmetry for mechanico–electrical systems with fractional derivatives

Zhang Shi-Hua (张世华)^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:2012-03-04 Revised:2012-04-23 Online:2012-09-01 Published:2012-09-01
Contact: Fu Jing-Li E-mail:sqfujngli@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11072218 and 60575055).

摘要/Abstract

摘要： This paper presents extensions to the traditional calculus of variations for mechanico-electrical systems containing fractional derivatives. The Euler-Lagrange equations and the Hamilton formalism of the mechanico-electrical systems with fractional derivatives are established. The definition and the criteria for the fractional generalized Noether quasi-symmetry are presented. Furthermore, the fractional Noether theorem and conseved quantities of the systems are obtained by virtue of the invariance of the Hamiltonian action under the infinitesimal transformations. An example is presented to illustrate the application of the results.

关键词: fractional derivative, mechanico-electrical system, Noether symmetry, Hamiltonian formulation

Abstract: This paper presents extensions to the traditional calculus of variations for mechanico-electrical systems containing fractional derivatives. The Euler-Lagrange equations and the Hamilton formalism of the mechanico-electrical systems with fractional derivatives are established. The definition and the criteria for the fractional generalized Noether quasi-symmetry are presented. Furthermore, the fractional Noether theorem and conseved quantities of the systems are obtained by virtue of the invariance of the Hamiltonian action under the infinitesimal transformations. An example is presented to illustrate the application of the results.

Key words: fractional derivative, mechanico-electrical system, Noether symmetry, Hamiltonian formulation

中图分类号: (Group theory)

02.20.-a

11.10.Ef (Lagrangian and Hamiltonian approach) 11.30.-j (Symmetry and conservation laws)

张世华, 陈本永, 傅景礼. Hamilton formalism and Noether symmetry for mechanico–electrical systems with fractional derivatives[J]. 中国物理B, 2012, 21(10): 100202-100202.

Zhang Shi-Hua (张世华), Chen Ben-Yong (陈本永), Fu Jing-Li (傅景礼). Hamilton formalism and Noether symmetry for mechanico–electrical systems with fractional derivatives[J]. Chin. Phys. B, 2012, 21(10): 100202-100202.

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Hamilton formalism and Noether symmetry for mechanico–electrical systems with fractional derivatives

Hamilton formalism and Noether symmetry for mechanico–electrical systems with fractional derivatives

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