In this paper, we focus on studying the fractional variational principle and the differential equations of motion for a fractional mechanical system. A combined Riemann-Liouville fractional derivative operator is defi...In this paper, we focus on studying the fractional variational principle and the differential equations of motion for a fractional mechanical system. A combined Riemann-Liouville fractional derivative operator is defined, and a fractional Hamilton principle under this definition is established. The fractional Lagrange equations and the fractional Hamilton canonical equations are derived from the fractional Hamilton principle. A number of special cases are given, showing the universality of our conclusions. At the end of the paper, an example is given to illustrate the application of the results.展开更多
Noether theorems for two fractional singular systems are discussed.One system involves mixed integer and Caputo fractional derivatives,and the other involves only Caputo fractional derivatives.Firstly,the fractional p...Noether theorems for two fractional singular systems are discussed.One system involves mixed integer and Caputo fractional derivatives,and the other involves only Caputo fractional derivatives.Firstly,the fractional primary constraints and the fractional constrained Hamilton equations are given.Then,the fractional Noether theorems of the two fractional singular systems are established,including the fractional Noether identities,the fractional Noether quasi-identities and the fractional conserved quantities.Finally,the results obtained are illustrated by two examples.展开更多
Singular system has great relationship with gauge field theory,condensed matter theory and some other research areas.Based on the mixed integer and Riemann-Liouville fractional derivatives,the fractional singular syst...Singular system has great relationship with gauge field theory,condensed matter theory and some other research areas.Based on the mixed integer and Riemann-Liouville fractional derivatives,the fractional singular system is studied.Firstly,the fractional constrained Hamilton equation and the fractional inherent constraint are presented.Secondly,Lie symmetry and conserved quantity are analyzed,including determined equation,limited equation,additional limited equation and structural equation.And finally,an example is given to illustrate the methods and results.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 10972151)
文摘In this paper, we focus on studying the fractional variational principle and the differential equations of motion for a fractional mechanical system. A combined Riemann-Liouville fractional derivative operator is defined, and a fractional Hamilton principle under this definition is established. The fractional Lagrange equations and the fractional Hamilton canonical equations are derived from the fractional Hamilton principle. A number of special cases are given, showing the universality of our conclusions. At the end of the paper, an example is given to illustrate the application of the results.
基金Supported by the National Natural Science Foundation of China(12172241,12002228,12272248,11972241)Qing Lan Project of Colleges and Universities in Jiangsu Province
文摘Noether theorems for two fractional singular systems are discussed.One system involves mixed integer and Caputo fractional derivatives,and the other involves only Caputo fractional derivatives.Firstly,the fractional primary constraints and the fractional constrained Hamilton equations are given.Then,the fractional Noether theorems of the two fractional singular systems are established,including the fractional Noether identities,the fractional Noether quasi-identities and the fractional conserved quantities.Finally,the results obtained are illustrated by two examples.
基金the National Natural Science Foundation of China(12172241,11802193,11972241)the Natural Science Foundation of Jiangsu Province(BK20191454)the"Qinglan Project"of Jiangsu Province。
文摘Singular system has great relationship with gauge field theory,condensed matter theory and some other research areas.Based on the mixed integer and Riemann-Liouville fractional derivatives,the fractional singular system is studied.Firstly,the fractional constrained Hamilton equation and the fractional inherent constraint are presented.Secondly,Lie symmetry and conserved quantity are analyzed,including determined equation,limited equation,additional limited equation and structural equation.And finally,an example is given to illustrate the methods and results.
