This paper investigates the Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems. The variational principle of discrete mechanics, from which discrete motion equations of sys...This paper investigates the Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems. The variational principle of discrete mechanics, from which discrete motion equations of systems are deduced, is generalized to the case of including the time variational. The requirement for an invariant group transformation is defined to be the Lie symmetry and the criterion when the Noether conserved quantities may be obtained from Lie symmetries is also presented. An example is discussed for applications of the results.展开更多
The Mei symmetry and conserved quantity of general discrete holonomic system are investigated in thispaper.The requirement for an invariant formalism of discrete motion equations is defined to be Mei symmetry.Thecrite...The Mei symmetry and conserved quantity of general discrete holonomic system are investigated in thispaper.The requirement for an invariant formalism of discrete motion equations is defined to be Mei symmetry.Thecriterion when a conserved quantity may be obtained from Mei symmetry is also deduced.An example is discussed forapplications of the results.展开更多
The Noether symmetry, the Lie symmetry and the conserved quantity of discrete holonomic systems with dependent coordinates are investigated in this paper. The Noether symmetry provides a discrete Noether identity and ...The Noether symmetry, the Lie symmetry and the conserved quantity of discrete holonomic systems with dependent coordinates are investigated in this paper. The Noether symmetry provides a discrete Noether identity and a conserved quantity of the system. The invariance of discrete motion equations under infinitesimal transformation groups is defined as the Lie symmetry, and the condition of obtaining the Noether conserved quantity from the Lie symmetry is also presented. An example is discussed to show the applications of the results.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No 10672143)the Natural Science Foundation of Henan Province,China (Grant No 0511022200)
文摘This paper investigates the Lie symmetries and Noether conserved quantities of discrete non-conservative mechanical systems. The variational principle of discrete mechanics, from which discrete motion equations of systems are deduced, is generalized to the case of including the time variational. The requirement for an invariant group transformation is defined to be the Lie symmetry and the criterion when the Noether conserved quantities may be obtained from Lie symmetries is also presented. An example is discussed for applications of the results.
基金National Natural Science Foundation of China under Grant No.10672143
文摘The Mei symmetry and conserved quantity of general discrete holonomic system are investigated in thispaper.The requirement for an invariant formalism of discrete motion equations is defined to be Mei symmetry.Thecriterion when a conserved quantity may be obtained from Mei symmetry is also deduced.An example is discussed forapplications of the results.
基金supported by the National Natural Science Foundation of China (Grant No 10672143)
文摘The Noether symmetry, the Lie symmetry and the conserved quantity of discrete holonomic systems with dependent coordinates are investigated in this paper. The Noether symmetry provides a discrete Noether identity and a conserved quantity of the system. The invariance of discrete motion equations under infinitesimal transformation groups is defined as the Lie symmetry, and the condition of obtaining the Noether conserved quantity from the Lie symmetry is also presented. An example is discussed to show the applications of the results.
