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 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
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 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
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
For a perturbed mechanical system in phase space, considering d/dt in the structure equation and process of proof including infinitesimal parameter ε obviously, this paper studies the perturbation to Mei symmetry and...For a perturbed mechanical system in phase space, considering d/dt in the structure equation and process of proof including infinitesimal parameter ε obviously, this paper studies the perturbation to Mei symmetry and adiabatic invariants. Firstly, the exact invariant induced directly from the Mei symmetry of the system without perturbation is given. Secondly, based on the concept of high-order adiabatic invariant, the determining equations of the perturbation to Mei symmetry are established, the condition of existence of the Mei adiabatic invariant led by the perturbation to Mei symmetry is obtained, and its form is presented. Lastly, 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
Based on the concept of discrete adiabatic invariant, this paper studies the perturbation to Mei symmetry and Mei adiabatic invariants of the discrete generalized Birkhoffian system. The discrete Mei exact invariant i...Based on the concept of discrete adiabatic invariant, this paper studies the perturbation to Mei symmetry and Mei adiabatic invariants of the discrete generalized Birkhoffian system. The discrete Mei exact invariant induced from the Mei symmetry of the system without perturbation is given. The criterion of the perturbation to Mei symmetry is established and the discrete Mei adiabatic invariant induced from the perturbation to Mei symmetry is obtained. Meanwhile, an example is discussed to illustrate the application of the results.展开更多
Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system are investi- gated. Appell equations and differential equations of motion for a variable mass holonomic system are estab...Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system are investi- gated. Appell equations and differential equations of motion for a variable mass holonomic system are established. A new expression of the total first derivative of the function with respect of time t along the systematic motional track curve, and the definition and the criterion of Mei symmetry for Appell equations under the infinitesimal transformations of groups are given. The expressions of the structural equation and Mei conserved quantity for Mei symmetry in Appell are obtained. An example is 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
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
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
Based on the concept of adiabatic invariant, this paper studies the perturbation to Mei symmetry and adiabatic invariants for Hamilton systems. The exact invariants of Mei symmetry for the system without perturbation ...Based on the concept of adiabatic invariant, this paper studies the perturbation to Mei symmetry and adiabatic invariants for Hamilton systems. The exact invariants of Mei symmetry for the system without perturbation are given. The perturbation to Mei symmetry is discussed and the adiabatic invariants induced from the perturbation to Mei symmetry of the system are obtained.展开更多
We investigate the application of the Mei symmetry analysis in finding conserved quantities for the thin elastic rod statics. By using the Mei symmetry analysis, we have obtained the Jacobi integral and the cyclic int...We investigate the application of the Mei symmetry analysis in finding conserved quantities for the thin elastic rod statics. By using the Mei symmetry analysis, we have obtained the Jacobi integral and the cyclic integrals for a thin elastic rod with intrinsic twisting for both the cases of circular and non-circular cross sections. Our results can be easily reduced to the results without the intrinsic twisting that have been reported. Through calculation, we find that the Noether symmetry can be more directly and easily used than the Mei symmetry in finding the first integrals for the thin elastic rod. These first integrals will be helpful in the study of exact solutions and stability, as well as the numerical simulation of the elastic rod model for DNA.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
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 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 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, 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
In this paper,two types of new conserved quantities directly deduced by Mei symmetry in phase space arestudied.The conditions under which Mei symmetry can directly lead to the two types of new conserved quantities and...In this paper,two types of new conserved quantities directly deduced by Mei symmetry in phase space arestudied.The conditions under which Mei symmetry can directly lead to the two types of new conserved quantities andthe forms of the two types of new conserved quantities are given.An example is given to illustrate the application ofthe results.展开更多
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 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.
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 (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. 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For a perturbed mechanical system in phase space, considering d/dt in the structure equation and process of proof including infinitesimal parameter ε obviously, this paper studies the perturbation to Mei symmetry and adiabatic invariants. Firstly, the exact invariant induced directly from the Mei symmetry of the system without perturbation is given. Secondly, based on the concept of high-order adiabatic invariant, the determining equations of the perturbation to Mei symmetry are established, the condition of existence of the Mei adiabatic invariant led by the perturbation to Mei symmetry is obtained, and its form is presented. Lastly, 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Project supported by the Fundamental Research Funds for the Central Universities of China (Grant No. 09CX04018A)
文摘Based on the concept of discrete adiabatic invariant, this paper studies the perturbation to Mei symmetry and Mei adiabatic invariants of the discrete generalized Birkhoffian system. The discrete Mei exact invariant induced from the Mei symmetry of the system without perturbation is given. The criterion of the perturbation to Mei symmetry is established and the discrete Mei adiabatic invariant induced from the perturbation to Mei symmetry is obtained. Meanwhile, an example is discussed 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 Appell equations for a variable mass holonomic system are investi- gated. Appell equations and differential equations of motion for a variable mass holonomic system are established. A new expression of the total first derivative of the function with respect of time t along the systematic motional track curve, and the definition and the criterion of Mei symmetry for Appell equations under the infinitesimal transformations of groups are given. The expressions of the structural equation and Mei conserved quantity for Mei symmetry in Appell 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 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.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.
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Based on the concept of adiabatic invariant, this paper studies the perturbation to Mei symmetry and adiabatic invariants for Hamilton systems. The exact invariants of Mei symmetry for the system without perturbation are given. The perturbation to Mei symmetry is discussed and the adiabatic invariants induced from the perturbation to Mei symmetry of the system are obtained.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10972143)the Research Plan of Higher Education Institutions of Xinjiang Autonomous Region, China (Grand No. XJEDU2010S31)the Foundation for Key Subject of Theory Physics of Xinjiang Autonomous Region, China
文摘We investigate the application of the Mei symmetry analysis in finding conserved quantities for the thin elastic rod statics. By using the Mei symmetry analysis, we have obtained the Jacobi integral and the cyclic integrals for a thin elastic rod with intrinsic twisting for both the cases of circular and non-circular cross sections. Our results can be easily reduced to the results without the intrinsic twisting that have been reported. Through calculation, we find that the Noether symmetry can be more directly and easily used than the Mei symmetry in finding the first integrals for the thin elastic rod. These first integrals will be helpful in the study of exact solutions and stability, as well as the numerical simulation of the elastic rod model for DNA.
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.
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.
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.
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.
文摘In this paper,two types of new conserved quantities directly deduced by Mei symmetry in phase space arestudied.The conditions under which Mei symmetry can directly lead to the two types of new conserved quantities andthe forms of the two types of new conserved quantities are given.An example is given to illustrate the application ofthe results.