Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a ...Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.展开更多
Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformationsof groups is investigated.Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tz...Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformationsof groups is investigated.Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tzénoffequations are given.Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given.Hojman conserved quantity of Tzénoff equations for the system above through special Lie symmetry and Lie symmetryin the condition of special Mei symmetry respectively is obtained.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 focuses on studying the Lie symmetry and a conserved quantity of a system of first-order differential equations. The determining equations of the Lie symmetry for a system of first-order differential equati...This paper focuses on studying the Lie symmetry and a conserved quantity of a system of first-order differential equations. The determining equations of the Lie symmetry for a system of first-order differential equations, from which a kind of conserved quantity is deduced, are presented. And their general conclusion is applied to a Hamilton system, a Birkhoff system and a generalized Hamilton system. Two examples are given to illustrate the application of the results.展开更多
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 focuses on a new symmetry of Hamiltonian and its conserved quantity for a system of generalized classical mechanics. The differential equations of motion of the system are established. The definition and th...This paper focuses on a new symmetry of Hamiltonian and its conserved quantity for a system of generalized classical mechanics. The differential equations of motion of the system are established. The definition and the criterion of the symmetry of Hamiltonian of the system are given. A conserved quantity directly derived from the symmetry of Hamiltonian of the generalized classical mechanical system is given. Since a Hamilton system is a special case of the generalized classical mechanics, the results above are equally applicable to the Hamilton system. The results of the paper are the generalization of a theorem known for the existing nonsingular equivalent Lagrangian. Finally, two examples are given to illustrate the application of the results.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
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
Lie symmetry of Maggi equations is studied. Its determining equation and restriction equation of nonholonomic constraint are given. A Hojman conserved quantity can be deduced directly by using the Lie symmetry. An exa...Lie symmetry of Maggi equations is studied. Its determining equation and restriction equation of nonholonomic constraint are given. A Hojman conserved quantity can be deduced directly by using the Lie symmetry. An example is given to illustrate the application of the result.展开更多
Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomicsystems with unilateral constraints are investigated.Appell equations and differential equations of motion for holonomicm...Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomicsystems with unilateral constraints are investigated.Appell equations and differential equations of motion for holonomicmechanic systems with unilateral constraints are established.The definition and the criterion of Mei symmetry forAppell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups arealso given.The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equationsin holonomic systems with unilateral constraints expressed by Appell functions are obtained.An example is given toillustrate the application of the results.展开更多
沿着系统的轨道基于全部的时间衍生物,为非保守的动态系统,保存数量间接地从系统的谎言对称推出了的概括 Mei 被学习。第一,系统的谎言对称被给。然后,谎言对称是 Mei 对称的必要、足够的在下面条件被介绍,保存数量间接地从系统的...沿着系统的轨道基于全部的时间衍生物,为非保守的动态系统,保存数量间接地从系统的谎言对称推出了的概括 Mei 被学习。第一,系统的谎言对称被给。然后,谎言对称是 Mei 对称的必要、足够的在下面条件被介绍,保存数量间接地从系统的谎言对称推出了的概括 Mei 被获得。最后,一个例子被给说明结果的申请。展开更多
In this paper,the form invariance and the Lie symmetry of Lagrange's equations for nonconservativesystem in generalized classical mechanics under the infinitesimal transformations of group are studied,and the Noet...In this paper,the form invariance and the Lie symmetry of Lagrange's equations for nonconservativesystem in generalized classical mechanics under the infinitesimal transformations of group are studied,and the Noether'sconserved quantity,the new form conserved quantity,and the Hojman's conserved quantity of system are derived fromthem.Finally,an example is given to illustrate the application of the result.展开更多
The Noether symmetry, the Mei symmetry and the conserved quantities of discrete generalized Birkhoffian system are studied in this paper. Using the difference discrete variational approach, the difference discrete var...The Noether symmetry, the Mei symmetry and the conserved quantities of discrete generalized Birkhoffian system are studied in this paper. Using the difference discrete variational approach, the difference discrete variational principle of discrete generalized Birkhoffian system is derived. The discrete equations of motion of the system are established. The criterion of Noether symmetry and Mei symmetry of the system is given. The discrete Noether and Mei conserved quantities and the conditions for their existence are obtained. Finally, an example is given to show the applications of the results.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
In this paper,the Mei symmetry of Tzénoff equations for the higher-order nonholonomic system and the new conserved quantities derived from that are researched,and the function expression of new conserved quantiti...In this paper,the Mei symmetry of Tzénoff equations for the higher-order nonholonomic system and the new conserved quantities derived from that are researched,and the function expression of new conserved quantities and criterion equation which deduces these conserved quantities are presented.This result establishes the theory basis for further researches on conservation laws of Tzénoff equations of the higher-order nonholonomic constraint system.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
文摘Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.
基金National Natural Science Foundation of China under Grant No.10672143
文摘Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformationsof groups is investigated.Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tzénoffequations are given.Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given.Hojman conserved quantity of Tzénoff equations for the system above through special Lie symmetry and Lie symmetryin the condition of special Mei symmetry respectively is obtained.
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Project supported by the National Natural Science Foundation of China (Grant No 10272021) and the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022).
文摘This paper focuses on studying the Lie symmetry and a conserved quantity of a system of first-order differential equations. The determining equations of the Lie symmetry for a system of first-order differential equations, from which a kind of conserved quantity is deduced, are presented. And their general conclusion is applied to a Hamilton system, a Birkhoff system and a generalized Hamilton system. Two examples are given to illustrate the application of the results.
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.
基金supported by the National Natural Science Foundation of China (Grant No. 10972151)
文摘This paper focuses on a new symmetry of Hamiltonian and its conserved quantity for a system of generalized classical mechanics. The differential equations of motion of the system are established. The definition and the criterion of the symmetry of Hamiltonian of the system are given. A conserved quantity directly derived from the symmetry of Hamiltonian of the generalized classical mechanical system is given. Since a Hamilton system is a special case of the generalized classical mechanics, the results above are equally applicable to the Hamilton system. The results of the paper are the generalization of a theorem known for the existing nonsingular equivalent Lagrangian. Finally, two examples are given to illustrate the application of the results.
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 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Sponsored by the National Natural Science Foundation of China(10572021)
文摘Lie symmetry of Maggi equations is studied. Its determining equation and restriction equation of nonholonomic constraint are given. A Hojman conserved quantity can be deduced directly by using the Lie symmetry. An example is given to illustrate the application of the result.
基金Supported by the National Natural Science Foundation of China under Grant No.10572021the Preparatory Research Foundation of Jiangnan University under Grant No.2008LYY011
文摘Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomicsystems with unilateral constraints are investigated.Appell equations and differential equations of motion for holonomicmechanic systems with unilateral constraints are established.The definition and the criterion of Mei symmetry forAppell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups arealso given.The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equationsin holonomic systems with unilateral constraints expressed by Appell functions are obtained.An example is given toillustrate the application of the results.
基金Supported by the National Natural Science Foundation of China under Grant No.10572021the Preparatory Research Foundation of Jiangnan University under Grant No.2008LYY011
文摘沿着系统的轨道基于全部的时间衍生物,为非保守的动态系统,保存数量间接地从系统的谎言对称推出了的概括 Mei 被学习。第一,系统的谎言对称被给。然后,谎言对称是 Mei 对称的必要、足够的在下面条件被介绍,保存数量间接地从系统的谎言对称推出了的概括 Mei 被获得。最后,一个例子被给说明结果的申请。
基金National Natural Science Foundation of China under Grant No.10272034the Doctoral Program Foundation of China
文摘In this paper,the form invariance and the Lie symmetry of Lagrange's equations for nonconservativesystem in generalized classical mechanics under the infinitesimal transformations of group are studied,and the Noether'sconserved quantity,the new form conserved quantity,and the Hojman's conserved quantity of system are derived fromthem.Finally,an example is given to illustrate the application of the result.
基金Project supported by the Fundamental Research Funds for the Central Universities of China (Grant No. 09CX04018A)
文摘The Noether symmetry, the Mei symmetry and the conserved quantities of discrete generalized Birkhoffian system are studied in this paper. Using the difference discrete variational approach, the difference discrete variational principle of discrete generalized Birkhoffian system is derived. The discrete equations of motion of the system are established. The criterion of Noether symmetry and Mei symmetry of the system is given. The discrete Noether and Mei conserved quantities and the conditions for their existence are obtained. Finally, an example is given to show the applications of the results.
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.10972127)
文摘In this paper,the Mei symmetry of Tzénoff equations for the higher-order nonholonomic system and the new conserved quantities derived from that are researched,and the function expression of new conserved quantities and criterion equation which deduces these conserved quantities are presented.This result establishes the theory basis for further researches on conservation laws of Tzénoff equations of the higher-order nonholonomic constraint system.
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.