This paper studies conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems. The definition and the determining equation of conformal invariance for mechanico-electrical systems...This paper studies conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems. The definition and the determining equation of conformal invariance for mechanico-electrical systems are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry under the infinitesimal single- parameter transformation group. The generalized Hojman conserved quantities from the conformal invariance of the system are given. An example is given to illustrate the application of the result.展开更多
We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico--electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-elec...We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico--electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-electrical coupling dynamical systems is given. Simultaneously, the condition of existence of the new conserved quantity of Mei symmetry for mechanico-electrical coupling dynamical systems is obtained. Finally, an example is given to illustrate the application of the results.展开更多
This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems,which leave invuriant the set of solutions of the corresponding diffe...This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems,which leave invuriant the set of solutions of the corresponding difference scheme. This approach makes it possible to devise techniques for solving the Lagrange Maxwell equations in differences which correspond to mechanico-electrical systems,by adapting existing differential equations.In particular,it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical systems.As an application,it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone.展开更多
The unified symmetry of mechano-electrical systems with nonholonomic constraints are studied in this paper, the definition and the criterion of unified symmetry of mechano-electrical systems with nonholonomic constrai...The unified symmetry of mechano-electrical systems with nonholonomic constraints are studied in this paper, the definition and the criterion of unified symmetry of mechano-electrical systems with nonholonomic constraints are derived from the Lagrange-Maxwell equations. The Noether conserved quantity, Hojman conserved quantity and Mei conserved quantity are then deduced from the unified symmetry. An example is given to illustrate the application of the results.展开更多
Noether-Mei symmetry of a discrete mechanico-electrical system on a regular lattice is investigated. Firstly, the Noether symmetry of a discrete mechanico-electrical system is reviewed, and the motion equations and en...Noether-Mei symmetry of a discrete mechanico-electrical system on a regular lattice is investigated. Firstly, the Noether symmetry of a discrete mechanico-electrical system is reviewed, and the motion equations and energy equations are derived. Secondly, the definition of Noether-Mei symmetry for the system is presented, and the criterion is derived. Thirdly, conserved quantities induced by Noether Mei symmetry with their existence conditions are obtained. Finally, an example is discussed to illustrate the results.展开更多
We study the approximate conserved quantity of the weakly nonholonomic mechanical-electrical system. By means of the Lagrange-Maxwell equation, the Noether equality of the weakly nonholonomic mechanical-electrical sys...We study the approximate conserved quantity of the weakly nonholonomic mechanical-electrical system. By means of the Lagrange-Maxwell equation, the Noether equality of the weakly nonholonomic mechanical-electrical system is obtained. The multiple powers-series expansion of the parameter of the generators of infinitesimal transformations and the gauge function is put into a generalized Noether identity. Using the Noether theorem, we obtain an approximate conserved quantity. An example is provided to prove the existence of the approximate conserved quantity.展开更多
文摘This paper studies conformal invariance and generalized Hojman conserved quantities of mechanico-electrical systems. The definition and the determining equation of conformal invariance for mechanico-electrical systems are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry under the infinitesimal single- parameter transformation group. The generalized Hojman conserved quantities from the conformal invariance of the system are given. An example is given to illustrate the application of the result.
基金supported by the National Natural Science Foundation of China (Grant No.11072218)
文摘We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico--electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-electrical coupling dynamical systems is given. Simultaneously, the condition of existence of the new conserved quantity of Mei symmetry for mechanico-electrical coupling dynamical systems is 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 (Grants Nos 10672143 and 60575055)State Key Laboratory of Scientific and Engineering Computing,Chinese Academy of Sciences+1 种基金Tang Yi-Fa acknowledges the support under Sabbatical Program (SAB2006-0070) of the Spanish Ministry of Education and ScienceJimnez S and Vzquez L acknowledge support of the Spanish Ministry of Education and Science (Grant No MTM2005-05573)
文摘This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems,which leave invuriant the set of solutions of the corresponding difference scheme. This approach makes it possible to devise techniques for solving the Lagrange Maxwell equations in differences which correspond to mechanico-electrical systems,by adapting existing differential equations.In particular,it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical systems.As an application,it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone.
文摘The unified symmetry of mechano-electrical systems with nonholonomic constraints are studied in this paper, the definition and the criterion of unified symmetry of mechano-electrical systems with nonholonomic constraints are derived from the Lagrange-Maxwell equations. The Noether conserved quantity, Hojman conserved quantity and Mei conserved quantity are then deduced from the unified symmetry. An example is given to illustrate the application of the results.
基金Project supported by the Natural Science Foundation of Shandong Province of China (Grant No. ZR2011AM012)
文摘Noether-Mei symmetry of a discrete mechanico-electrical system on a regular lattice is investigated. Firstly, the Noether symmetry of a discrete mechanico-electrical system is reviewed, and the motion equations and energy equations are derived. Secondly, the definition of Noether-Mei symmetry for the system is presented, and the criterion is derived. Thirdly, conserved quantities induced by Noether Mei symmetry with their existence conditions are obtained. Finally, an example is discussed to illustrate the results.
文摘We study the approximate conserved quantity of the weakly nonholonomic mechanical-electrical system. By means of the Lagrange-Maxwell equation, the Noether equality of the weakly nonholonomic mechanical-electrical system is obtained. The multiple powers-series expansion of the parameter of the generators of infinitesimal transformations and the gauge function is put into a generalized Noether identity. Using the Noether theorem, we obtain an approximate conserved quantity. An example is provided to prove the existence of the approximate conserved quantity.