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
In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e. a Noether-Lie symmetry, is presented, and the criterion o...In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e. a Noether-Lie symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the generalized Hojman conserved quantity of the Noether Lie symmetry of the system are obtained. The Noether-Lie symmetry contains the Noether symmetry and the Lie symmetry, and has more generalized significance.展开更多
Singular systems within combined fractional derivatives are established.Firstly,the fractional Lagrange equation is analyzed.Secondly,the fractional primary constraint is given.Thirdly,the Noether and Lie symmetry met...Singular systems within combined fractional derivatives are established.Firstly,the fractional Lagrange equation is analyzed.Secondly,the fractional primary constraint is given.Thirdly,the Noether and Lie symmetry methods of fractional constrained Hamiltonian system are studied.Finally,the obtained results are illustrated with an example.展开更多
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.
文摘In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e. a Noether-Lie symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the generalized Hojman conserved quantity of the Noether Lie symmetry of the system are obtained. The Noether-Lie symmetry contains the Noether symmetry and the Lie symmetry, and has more generalized significance.
基金Supported by the National Natural Science Foundation of China (12172241, 12272248)the Qing Lan Project of Colleges and Universities in Jiangsu Province。
文摘Singular systems within combined fractional derivatives are established.Firstly,the fractional Lagrange equation is analyzed.Secondly,the fractional primary constraint is given.Thirdly,the Noether and Lie symmetry methods of fractional constrained Hamiltonian system are studied.Finally,the obtained results are illustrated with an example.
