Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a...Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given. Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained. Finally, an example is given to illustrate the application of the results.展开更多
This paper studies the Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass. The discrete Euler-Lagrange equation and energy evolution equation are derived by using a total...This paper studies the Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass. The discrete Euler-Lagrange equation and energy evolution equation are derived by using a total variational principle. The invariance of discrete equations under infinitesimal transformation groups is defined to be Lie symmetry. The condition of obtaining the Noether conserved quantities from the Lie symmetries is also presented. An example is discussed for applications of the results.展开更多
In this paper the conformal invariance by infinitesimal transformations of first-order Lagrange systems is discussed in detail. The necessary and sumeient conditions of conformal invariance by the action of infinitesi...In this paper the conformal invariance by infinitesimal transformations of first-order Lagrange systems is discussed in detail. The necessary and sumeient conditions of conformal invariance by the action of infinitesimal transformations being Lie symmetry simultaneously are given. Then we get the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.展开更多
To study Lie symmetry and the conserved quantity of a generalized Birkhoff system with additional terms, the determining equations of the Lie symmetry of the system is derived. A con- served quantity of Hojman＇ s typ...To study Lie symmetry and the conserved quantity of a generalized Birkhoff system with additional terms, the determining equations of the Lie symmetry of the system is derived. A con- served quantity of Hojman＇ s type and a Noether＇ s conserved quantity are deduced by the Lie symme- try under some conditions. One example is given to illustrate the application of the result.展开更多
In this paper, the Noether Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general in...In this paper, the Noether Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether Lie symmetry are obtained. An example is given to illustrate the application of the results.展开更多
The variational calculus of time-scale non-shifted systems includes both the traditional continuous and traditional significant discrete variational calculus.Not only can the combination ofand∇derivatives be beneficia...The variational calculus of time-scale non-shifted systems includes both the traditional continuous and traditional significant discrete variational calculus.Not only can the combination ofand∇derivatives be beneficial to obtaining higher convergence order in numerical analysis,but also it prompts the timescale numerical computational scheme to have good properties,for instance,structure-preserving.In this letter,a structure-preserving algorithm for time-scale non-shifted Hamiltonian systems is proposed.By using the time-scale discrete variational method and calculus theory,and taking a discrete time scale in the variational principle of non-shifted Hamiltonian systems,the corresponding discrete Hamiltonian principle can be obtained.Furthermore,the time-scale discrete Hamilton difference equations,Noether theorem,and the symplectic scheme of discrete Hamiltonian systems are obtained.Finally,taking the Kepler problem and damped oscillator for time-scale non-shifted Hamiltonian systems as examples,they show that the time-scale discrete variational method is a structure-preserving algorithm.The new algorithm not only provides a numerical method for solving time-scale non-shifted dynamic equations but can be calculated with variable step sizes to improve the computational speed.展开更多
Under the assumption that the growth order of the free term to satisfy the natural growth condition with respect to gradient of the generalized solutions, the maximum principle is proved for the bounded generalized so...Under the assumption that the growth order of the free term to satisfy the natural growth condition with respect to gradient of the generalized solutions, the maximum principle is proved for the bounded generalized solution of quasi_linear elliptic equations.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10572021the Preparatory Research Foundation of Jiangnan University under Grant No.2008LYY011
文摘Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given. Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained. Finally, an example is given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China(Grant No10672143)
文摘This paper studies the Lie symmetries and Noether conserved quantities of discrete mechanical systems with variable mass. The discrete Euler-Lagrange equation and energy evolution equation are derived by using a total variational principle. The invariance of discrete equations under infinitesimal transformation groups is defined to be Lie symmetry. The condition of obtaining the Noether conserved quantities from the Lie symmetries is also presented. An example is discussed for applications of the results.
基金supported by National Natural Science Foundation of China under Grant Nos.10472040,10572021,and 10772025the Outstanding Young Talents Training Fund of Liaoning Province of China under Grant No.3040005
文摘In this paper the conformal invariance by infinitesimal transformations of first-order Lagrange systems is discussed in detail. The necessary and sumeient conditions of conformal invariance by the action of infinitesimal transformations being Lie symmetry simultaneously are given. Then we get the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.
基金Supported by the National Natural Science Foundation of China(10772025)the Key Program of the National Natural Science Foundation of China(10932002)
文摘To study Lie symmetry and the conserved quantity of a generalized Birkhoff system with additional terms, the determining equations of the Lie symmetry of the system is derived. A con- served quantity of Hojman＇ s type and a Noether＇ s conserved quantity are deduced by the Lie symme- try under some conditions. One example is given to illustrate the application of the result.
文摘In this paper, the Noether Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether Lie symmetry are obtained. An example is given to illustrate the application of the results.
基金This work was supported by the National Natural Science Foundation of China(Nos.11972241,11572212)the Natural Science Foundation of Jiangsu Province(No.BK20191454)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(No.KYCX20_0251).
文摘The variational calculus of time-scale non-shifted systems includes both the traditional continuous and traditional significant discrete variational calculus.Not only can the combination ofand∇derivatives be beneficial to obtaining higher convergence order in numerical analysis,but also it prompts the timescale numerical computational scheme to have good properties,for instance,structure-preserving.In this letter,a structure-preserving algorithm for time-scale non-shifted Hamiltonian systems is proposed.By using the time-scale discrete variational method and calculus theory,and taking a discrete time scale in the variational principle of non-shifted Hamiltonian systems,the corresponding discrete Hamiltonian principle can be obtained.Furthermore,the time-scale discrete Hamilton difference equations,Noether theorem,and the symplectic scheme of discrete Hamiltonian systems are obtained.Finally,taking the Kepler problem and damped oscillator for time-scale non-shifted Hamiltonian systems as examples,they show that the time-scale discrete variational method is a structure-preserving algorithm.The new algorithm not only provides a numerical method for solving time-scale non-shifted dynamic equations but can be calculated with variable step sizes to improve the computational speed.
文摘Under the assumption that the growth order of the free term to satisfy the natural growth condition with respect to gradient of the generalized solutions, the maximum principle is proved for the bounded generalized solution of quasi_linear elliptic equations.
