A type of new conserved quantity deduced from Mei symmetry of Appell equations for a holonomic system with unilateral constraints is investigated. The expressions of new structural equation and new conserved quantity ...A type of new conserved quantity deduced from Mei symmetry of Appell equations for a holonomic system with unilateral constraints is investigated. The expressions of new structural equation and new conserved quantity deduced from Mei symmetry of Appell equations for a holonomic system with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results.展开更多
This paper studies a new type of conserved quantity which is directly induced by Mei symmetry of the Lagrange system. Firstly, the definition and criterion of Mei symmetry for the Lagrange system are given. Secondly, ...This paper studies a new type of conserved quantity which is directly induced by Mei symmetry of the Lagrange system. Firstly, the definition and criterion of Mei symmetry for the Lagrange system are given. Secondly, a coordination function is introduced, and the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, an illustrated example is given. The result indicates that the coordination function can be selected properly according to the demand for finding the gauge function, and thereby the gauge function can be found more easily. Furthermore, since the choice of the coordination function has multiformity, many more conserved quantities of Mei symmetry for the Lagrange system can be obtained.展开更多
This paper studies a new type of conserved quantity which is directly induced by Lie symmetry of the Lagrange system. Firstly, the criterion of Lie symmetry for the Lagrange system is given. Secondly, the conditions o...This paper studies a new type of conserved quantity which is directly induced by Lie symmetry of the Lagrange system. Firstly, the criterion of Lie symmetry for the Lagrange system is given. Secondly, the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, 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 studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the ...This paper studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the existence of the new conserved quantities as well as their forms are proposed. Some special cases are given to illustrate the generalized significance of the new type conserved quantity. Finally, an illustrated example is given to show the application of the nonholonomic system＇s results.展开更多
In this paper, a new type of conserved quantity induced directly from the Mei symmetry for a relativistic nonholonomic mechanical system in phase space is studied. The definition and the criterion of the Mei symmetry ...In this paper, a new type of conserved quantity induced directly from the Mei symmetry for a relativistic nonholonomic mechanical system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions for the existence and form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.展开更多
This paper studies the Hojman conserved quantity, a non-Noether conserved quantity, deduced by special weak Noether symmetry for Lagrange systems. Under special infinitesimal transformations in which the time is not v...This paper studies the Hojman conserved quantity, a non-Noether conserved quantity, deduced by special weak Noether symmetry for Lagrange systems. Under special infinitesimal transformations in which the time is not variable, its criterion is given and a method of how to seek the Hojman conserved quantity is presented. A Hojman conserved quantity can be found by using the special weak Noether symmetry.展开更多
A type of structural equation and conserved quantity which are directly induced by Mei symmetry of Nielsen equations for a holonomic system are studied. Under the infinitesimal transformation of the groups, from the d...A type of structural equation and conserved quantity which are directly induced by Mei symmetry of Nielsen equations for a holonomic system are studied. Under the infinitesimal transformation of the groups, from the definition and the criterion of Mei symmetry, a type of structural equation and conserved quantity for the system by proposition 2 are obtained, and the inferences in two special cases are given. Finally, an example is given to illustrate the application of the results.展开更多
This paper studies a new conserved quantity which can be called generalized Mei conserved quantity and directly deduced by Mei symmetry of Birkhoff system. The conditions under which the Mei symmetry can directly lead...This paper studies a new conserved quantity which can be called generalized Mei conserved quantity and directly deduced by Mei symmetry of Birkhoff system. The conditions under which the Mei symmetry can directly lead to generalized Mei conserved quantity and the form of generalized Mei conserved quantity are given. An example is given to illustrate the application of the results.展开更多
In this paper we introduce the new concept of the conformal invariance and the conserved quantities for Appell systems under second-class Mei symmetry. The one-parameter infinitesimal transformation group and infinite...In this paper we introduce the new concept of the conformal invariance and the conserved quantities for Appell systems under second-class Mei symmetry. The one-parameter infinitesimal transformation group and infinitesimal transformation vector of generator are described in detail. The conformal factor in the determining equations under second-class Mei symmetry is found. The relationship between Appell system＇s conformal invariance and Mei symmetry are discussed. And Appell system＇s conformal invariance under second-class Mei symmetry may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.展开更多
This paper proposes a new concept of the conformal invariance and the conserved quantities for Birkhoff systems under second-class Mei symmetry. The definition about conformal invariance of Birkhoff systems under seco...This paper proposes a new concept of the conformal invariance and the conserved quantities for Birkhoff systems under second-class Mei symmetry. The definition about conformal invariance of Birkhoff systems under second-class Mei symmetry is given. The conformal factor in the determining equations is found. The relationship between Birkhoff system＇s conformal invariance and second-class Mei symmetry are discussed. The necessary and sufficient conditions of conformal invaxiance, which are simultaneously of second-class symmetry, are given. And Birkhoff system＇s conformal invariance may lead to corresponding Mei conserved quantities, which is deduced directly from the second-class Mei symmetry when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.展开更多
This paper investigates structure equation and Mei conserved quantity of Mei symmetry of Appell equations for non-Chetaev nonholonomic systems. Appell equations and differential equations of motion for non-Chetaev non...This paper investigates structure equation and Mei conserved quantity of Mei symmetry of Appell equations for non-Chetaev nonholonomic systems. Appell equations and differential equations of motion for non-Chetaev nonholonomic mechanical systems are established. A new expression of the total derivative of the function with respect to time t along the trajectory of a curve of the system is obtained, the definition and the criterion of Mei symmetry of Appell equations under the infinitesimal transformations of groups are also given. The expressions of the structure equation and the Mei conserved quantity of Mei symmetry in the Appell function are obtained. An example is given to illustrate the application of the results.展开更多
This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The defini...This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.展开更多
This paper studies two new types of conserved quantities deduced by Noether Mei symmetry of mechanical system in phase space. The definition and criterion of Noether Mei symmetry for the system are given. A coordinati...This paper studies two new types of conserved quantities deduced by Noether Mei symmetry of mechanical system in phase space. The definition and criterion of Noether Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether- Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether Mei symmetry of mechanical system can be obtained.展开更多
Mei symmetry and Mei conserved quantity of Nielsen equations for a non-holonomic, non-conservative system of Chetaev＇s type with variable mass are studied. The differential equations of motion of the Nielsen equation...Mei symmetry and Mei conserved quantity of Nielsen equations for a non-holonomic, non-conservative system of Chetaev＇s type with variable mass are studied. The differential equations of motion of the Nielsen equation for the system, the definition and criterion of Mei symmetry, and the condition and the form of Mei conserved quantity deduced directly by Mei symmetry for the system are obtained. An example is given to illustrate the application of the results.展开更多
This paper studies Mei symmetry which leads to a generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints. The differential equations of motion for the systems are establis...This paper studies Mei symmetry which leads to a generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints. The differential equations of motion for the systems are established, the definition and criterion of the Mei symmetry for the systems are given. The necessary and sufficient condition under which the Mei symmetry is a Lie symmetry for the systems is obtained and a generalized Hojman conserved quantity deduced from the Mei symmetry is got. An example is given to illustrate the application of the results.展开更多
In this paper,we investigate whether the Lie symmetry can induce the Mei conserved quantity directly in a nonconservative Hamilton system and a theorem is presented.The condition under which the Lie symmetry of the sy...In this paper,we investigate whether the Lie symmetry can induce the Mei conserved quantity directly in a nonconservative Hamilton system and a theorem is presented.The condition under which the Lie symmetry of the system directly induces the Mei conserved quantity is given.Meanwhile,an example is discussed to illustrate the application of the results.The present results have shown that the Lie symmetry of a nonconservative Hamilton system can also induce the Mei conserved quantity directly.展开更多
The Mei symmetry and Mei conserved quantity of the Nielsen equation for a non-Chetaewtype non-holonomic non-conservative system are studied. The differential equations of motion of the Nielsen equation for the system,...The Mei symmetry and Mei conserved quantity of the Nielsen equation for a non-Chetaewtype non-holonomic non-conservative system are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Mei symmetry and the condition and the form of Mei conserved quantities deduced directly from the Mei symmetry for the system are obtained. Finally, an example is given to illustrate the application of the results.展开更多
The Mei symmetry of Tzénoff equations under the infinitesimal transformations of groups is studied in this paper. The definition and the criterion equations of the symmetry are given. If the symmetry is a Noether...The Mei symmetry of Tzénoff equations under the infinitesimal transformations of groups is studied in this paper. The definition and the criterion equations of the symmetry are given. If the symmetry is a Noether symmetry, then the Noether conserved quantity of the Tzénoff equations can be obtained by the Mei symmetry.展开更多
This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system. On the basis of the form invariance of differential equations of m...This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system. On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation, the determining equations, the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed. The criterions of Mei symmetries, weak Mei symmetries and strong Mei symmetries of the system are given. New types of conserved quantities, i.e. the Mei symmetrical conserved quantities, the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system, are obtained. Then, a deduction of the first-order nonholonomic system is discussed. Finally, two examples are given to illustrate the application of the method and then the results.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 10572021)the Preparatory Research Foundation of Jiangnan University of China (Grant No. 2008LYY011)
文摘A type of new conserved quantity deduced from Mei symmetry of Appell equations for a holonomic system with unilateral constraints is investigated. The expressions of new structural equation and new conserved quantity deduced from Mei symmetry of Appell equations for a holonomic system with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results.
文摘This paper studies a new type of conserved quantity which is directly induced by Mei symmetry of the Lagrange system. Firstly, the definition and criterion of Mei symmetry for the Lagrange system are given. Secondly, a coordination function is introduced, and the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, an illustrated example is given. The result indicates that the coordination function can be selected properly according to the demand for finding the gauge function, and thereby the gauge function can be found more easily. Furthermore, since the choice of the coordination function has multiformity, many more conserved quantities of Mei symmetry for the Lagrange system can be obtained.
文摘This paper studies a new type of conserved quantity which is directly induced by Lie symmetry of the Lagrange system. Firstly, the criterion of Lie symmetry for the Lagrange system is given. Secondly, the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, 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.
文摘This paper studies the new type of conserved quantity which is directly induced by Mei symmetry of nonholonomic systems in terms of quasi-coordinates. A coordination function is introduced, and the conditions for the existence of the new conserved quantities as well as their forms are proposed. Some special cases are given to illustrate the generalized significance of the new type conserved quantity. Finally, an illustrated example is given to show the application of the nonholonomic system＇s results.
文摘In this paper, a new type of conserved quantity induced directly from the Mei symmetry for a relativistic nonholonomic mechanical system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions for the existence and form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022)
文摘This paper studies the Hojman conserved quantity, a non-Noether conserved quantity, deduced by special weak Noether symmetry for Lagrange systems. Under special infinitesimal transformations in which the time is not variable, its criterion is given and a method of how to seek the Hojman conserved quantity is presented. A Hojman conserved quantity can be found by using the special weak Noether symmetry.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11142014 and 61178032)
文摘A type of structural equation and conserved quantity which are directly induced by Mei symmetry of Nielsen equations for a holonomic system are studied. Under the infinitesimal transformation of the groups, from the definition and the criterion of Mei symmetry, a type of structural equation and conserved quantity for the system by proposition 2 are obtained, and the inferences in two special cases are given. Finally, an example is given to illustrate the application of the results.
基金Project supported by the Scientific Research Fund for Outstanding Young Teachers (Grant No XJNU0817)Fund for Prior Development Subject of Xinjiang Normal University and National Natural Science Foundation of China (Grant No 10864007)
文摘This paper studies a new conserved quantity which can be called generalized Mei conserved quantity and directly deduced by Mei symmetry of Birkhoff system. The conditions under which the Mei symmetry can directly lead to generalized Mei conserved quantity and the form of generalized Mei conserved quantity are given. An example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant Nos.10672143 and 60575055)
文摘In this paper we introduce the new concept of the conformal invariance and the conserved quantities for Appell systems under second-class Mei symmetry. The one-parameter infinitesimal transformation group and infinitesimal transformation vector of generator are described in detail. The conformal factor in the determining equations under second-class Mei symmetry is found. The relationship between Appell system＇s conformal invariance and Mei symmetry are discussed. And Appell system＇s conformal invariance under second-class Mei symmetry may lead to corresponding Hojman conserved quantities when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.
基金supported by the National Natural Science Foundation of China (Grant No. 11072218)the Natural Science Foundation of Zhejiang Province of China (Grant No. Y6100337)
文摘This paper proposes a new concept of the conformal invariance and the conserved quantities for Birkhoff systems under second-class Mei symmetry. The definition about conformal invariance of Birkhoff systems under second-class Mei symmetry is given. The conformal factor in the determining equations is found. The relationship between Birkhoff system＇s conformal invariance and second-class Mei symmetry are discussed. The necessary and sufficient conditions of conformal invaxiance, which are simultaneously of second-class symmetry, are given. And Birkhoff system＇s conformal invariance may lead to corresponding Mei conserved quantities, which is deduced directly from the second-class Mei symmetry when the conformal invariance satisfies some conditions. Lastly, an example is provided to illustrate the application of the result.
基金Project supported by the National Natural Science Foundation of China (Grant No 10572021)
文摘This paper investigates structure equation and Mei conserved quantity of Mei symmetry of Appell equations for non-Chetaev nonholonomic systems. Appell equations and differential equations of motion for non-Chetaev nonholonomic mechanical systems are established. A new expression of the total derivative of the function with respect to time t along the trajectory of a curve of the system is obtained, the definition and the criterion of Mei symmetry of Appell equations under the infinitesimal transformations of groups are also given. The expressions of the structure equation and the Mei conserved quantity of Mei symmetry in the Appell function are obtained. An example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant No 10572021)
文摘This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.
文摘This paper studies two new types of conserved quantities deduced by Noether Mei symmetry of mechanical system in phase space. The definition and criterion of Noether Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether- Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether Mei symmetry of mechanical system can be obtained.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10572021)the Preparatory Research Foundation of Jiangnan University,China (Grant No. 2008LYY011)
文摘Mei symmetry and Mei conserved quantity of Nielsen equations for a non-holonomic, non-conservative system of Chetaev＇s type with variable mass are studied. The differential equations of motion of the Nielsen equation for the system, the definition and criterion of Mei symmetry, and the condition and the form of Mei conserved quantity deduced directly by Mei symmetry for the system are obtained. An example is given to illustrate the application of the results.
文摘This paper studies Mei symmetry which leads to a generalized Hojman conserved quantity for variable mass systems with unilateral holonomic constraints. The differential equations of motion for the systems are established, the definition and criterion of the Mei symmetry for the systems are given. The necessary and sufficient condition under which the Mei symmetry is a Lie symmetry for the systems is obtained and a generalized Hojman conserved quantity deduced from the Mei symmetry is got. An example is given to illustrate the application of the results.
基金Projct supported by the Natural Science Foundation of Shandong Province,China (Grant No. ZR2011AM012)the Fundamental Research Funds for the Central Universities,China (Grant No. 09CX04018A)
文摘In this paper,we investigate whether the Lie symmetry can induce the Mei conserved quantity directly in a nonconservative Hamilton system and a theorem is presented.The condition under which the Lie symmetry of the system directly induces the Mei conserved quantity is given.Meanwhile,an example is discussed to illustrate the application of the results.The present results have shown that the Lie symmetry of a nonconservative Hamilton system can also induce the Mei conserved quantity directly.
基金supported by the National Natural Science Foundation of China(Grant No 10572021)the Preparatory Research Foundation of Jiangnan University,China(Grant No 2008LYY011)
文摘The Mei symmetry and Mei conserved quantity of the Nielsen equation for a non-Chetaewtype non-holonomic non-conservative system are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Mei symmetry and the condition and the form of Mei conserved quantities deduced directly from the Mei symmetry 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 No 10372053） and the Natural Science Foundation of Henan Province, China （Grant No 0311011400）. We are grateful for the instruction and help of Professor Mei F X, in Beijing Institute of Technology.
文摘The Mei symmetry of Tzénoff equations under the infinitesimal transformations of groups is studied in this paper. The definition and the criterion equations of the symmetry are given. If the symmetry is a Noether symmetry, then the Noether conserved quantity of the Tzénoff equations can be obtained by the Mei symmetry.
基金supported by the National Natural Science Foundation of China (Grant No. 10372053)
文摘This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system. On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation, the determining equations, the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed. The criterions of Mei symmetries, weak Mei symmetries and strong Mei symmetries of the system are given. New types of conserved quantities, i.e. the Mei symmetrical conserved quantities, the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system, are obtained. Then, a deduction of the first-order nonholonomic system is discussed. Finally, two examples are given to illustrate the application of the method and then the results.
