Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglo...Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglotz type equations for nonholonomic systems are established.Then,the Noether symmetries are studied,and the conserved quantities are obtained.The results are extended to nonholonomic canonical systems,and the Herglotz type canonical equations and the Noether theorems are obtained.Two examples are provided to demonstrate the validity of the methods and results.展开更多
The method of integrating factors is used to study the conservation laws of the Herglotz type Birkhoffian systems in this paper.Firstly,the definition of the integrating factors of the Herglotz type Birkhoffian system...The method of integrating factors is used to study the conservation laws of the Herglotz type Birkhoffian systems in this paper.Firstly,the definition of the integrating factors of the Herglotz type Birkhoffian systems is given.Secondly,the relationship between the integrating factors and conservation laws is studied,and the conservation theorems of Herglotz type Birkhoff's equations and their inverse theorems are established.Thirdly,two types of generalized Killing equations for calculating integrating factors are given.Finally,as an example,a linear damped oscillator is taken.This example can be transformed into a Herglotz type Birkhoffian system.The resulting conservation theorems are used to find the conserved quantities for this example.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.12272248)the Postgraduate Research and Practice Innovation Program of Jiangsu Province of China(Grant No.KYCX23_3296).
文摘Fractional calculus is widely used to deal with nonconservative dynamics because of its memorability and non-local properties.In this paper,the Herglotz principle with generalized operators is discussed,and the Herglotz type equations for nonholonomic systems are established.Then,the Noether symmetries are studied,and the conserved quantities are obtained.The results are extended to nonholonomic canonical systems,and the Herglotz type canonical equations and the Noether theorems are obtained.Two examples are provided to demonstrate the validity of the methods and results.
基金Supported by the National Natural Science Foundation of China(12272248)。
文摘The method of integrating factors is used to study the conservation laws of the Herglotz type Birkhoffian systems in this paper.Firstly,the definition of the integrating factors of the Herglotz type Birkhoffian systems is given.Secondly,the relationship between the integrating factors and conservation laws is studied,and the conservation theorems of Herglotz type Birkhoff's equations and their inverse theorems are established.Thirdly,two types of generalized Killing equations for calculating integrating factors are given.Finally,as an example,a linear damped oscillator is taken.This example can be transformed into a Herglotz type Birkhoffian system.The resulting conservation theorems are used to find the conserved quantities for this example.
