For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,...For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of nonNoether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.展开更多
In the paper [J. of Beijing Institute of Technology 26 （2006） 285] the authors provided the definition of weakly Noether symmetry. We now discuss the weakly Noether symmetry for non-holonomic system of Chetaev＇s ty...In the paper [J. of Beijing Institute of Technology 26 （2006） 285] the authors provided the definition of weakly Noether symmetry. We now discuss the weakly Noether symmetry for non-holonomic system of Chetaev＇s type, and present expressions of three kinds of conserved quantities by weakly Noether symmetry. Finally, the application of this new result is shown by a practical example.展开更多
The definition and criterion of the Mei symmetry of a relativistic variable mass system are given. The relation between the Mei symmetry and the Noether symmetry of the system is found under infinitesimal transformati...The definition and criterion of the Mei symmetry of a relativistic variable mass system are given. The relation between the Mei symmetry and the Noether symmetry of the system is found under infinitesimal transformations of groups. The conserved quantities to which the Mei symmetry and Noether symmetry of the system lead are obtained.An example is given to illustrate the application of the result.展开更多
To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relati...To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established.展开更多
In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two ca...In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.展开更多
基金国家自然科学基金，湖南省自然科学基金，the Scientific Research Foundation of Education Burean of Hunan Province
文摘For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of nonNoether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.
基金National Natural Science Foundation of China under Grant Nos.10572021 and 10772025the Doctoral Program Foundation of the Institution of Higher Education of China under Grant No.20040007022
文摘In the paper [J. of Beijing Institute of Technology 26 （2006） 285] the authors provided the definition of weakly Noether symmetry. We now discuss the weakly Noether symmetry for non-holonomic system of Chetaev＇s type, and present expressions of three kinds of conserved quantities by weakly Noether symmetry. Finally, the application of this new result is shown by a practical example.
文摘The definition and criterion of the Mei symmetry of a relativistic variable mass system are given. The relation between the Mei symmetry and the Noether symmetry of the system is found under infinitesimal transformations of groups. The conserved quantities to which the Mei symmetry and Noether symmetry of the system lead are obtained.An example is given to illustrate the application of the result.
文摘To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established.
基金supported by the National Natural Science Foundations of China (Grant Nos.11072218 and 11272287)the Natural Science Foundations of Zhejiang Province of China (Grant No.Y6110314)
文摘In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.
