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

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...

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Bibliographic Details
Published inChinese physics B Vol. 21; no. 10; pp. 9 - 16
Main Author 张世华 陈本永 傅景礼
Format Journal Article
LanguageEnglish
Published 01.10.2012
Subjects
Calculus of variations
Criteria
Derivatives
Formalism
Invariance
Mathematical analysis
Noether定理
Noether对称性
Symmetry
Transformations
分数阶导数
应用程序
形式主义
拉格朗日方程
无限小变换
电气系统
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Summary: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.
Bibliography:Zhang Shi-Hua, Chen Ben-Yong, and Fu Jing-Li（1. Faculty of Mechanical-Engineering ＆ Automation, Zhejiang Sci-Tech University, Hangzhou 310018, China ;2. Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China）
fractional derivative, mechanico-electrical system, Noether symmetry, Hamiltonian formulation
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.
11-5639/O4
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/21/10/100202