A New Conservation Law Derived from Mei Symmetry for the System of Generalized Classical Mechanics

A new conservation theorem derived directly from Mei symmetry of the generalized classical mechanical system is presented. First, the differential equations of motion of the system are established, and the definition and criterion of Mei symmetry for the system of generalized classical mechanics are given, which are based upon the invariance of dynamical functions under infinitesimal transformations. Second, the condition under which a Mei symmetry can lead to a new conservation law is obtained and the form of the conservation law is presented. And finally, an example is given to illustrate the application of the results.     

Lie Symmetry and Generalized Mei Conserved Quantity for Nonconservative Dynamical System

Based on the total time derivative along the trajectory of the system, for noneonservative dynamical system, the generalized Mei conserved quantity indirectly deduced from the Lie symmetry of the system is studied. Firstly, the Lie symmetry of the system is given. Then, the necessary and sumeient condition under which the Lie symmetry is a Mei symmetry is presented and the generalized Mei conserved quantity indirectly deduced from the Lie symmetry of the system is obtained. Lastly, an example is given to illustrate the application of the result.     

相对论性力学系统的Mei对称性导致的新守恒律

研究相对论性力学系统的Mei对称性和守恒律．基于动力学函数在无限小变换下的不变性，建立了相对论性力学系统的Mei对称性的定义和判据；直接由相对论性力学系统的Mei对称性导出了一类新守恒律，给出了Mei对称性导致新守恒律的条件和新守恒律的形式，并举例说明结果的应用． 关键词： 相对论 力学系统 Mei对称性 守恒律     

Mei Symmetry of General Discrete Holonomic System

The Mei symmetry and conserved quantity of general discrete holonomic system are investigated in this paper. The requirement for an invariant formalism of discrete motion equations is defined to be Mei symmetry. The criterion when a conserved quantity may be obtained from Mei symmetry is also deduced. An example is discussed for applications of the results.     

Mei Symmetry of General Discrete Holonomic System

The Mei symmetry and conserved quantity of general discrete holonomic system are investigated in this paper. The requirement for an invariant formalism of discrete motion equations is defined to be Mei symmetry. The criterion when a conserved quantity may be obtained from Mei symmetry is also deduced. An example is discussed for applications of the results.     

Noether-Lie Symmetry of Generalized Classical Mechanical Systems

In this paper, the Noether Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether Lie symmetry are obtained. An example is given to illustrate the application of the results.     

A New Type of Conserved Quantity of Mei Symmetry for Lagrange Systems

A new type of conserved quantity, which is induced from the Mei symmetry of Lagrange systems, is studied. The conditions for that the new type of conserved quantity exists and the form of the new type of conserved quantity are obtained. An illustrated example is given. The Noether conserved quantity induced from the Mei symmetry of Lagrange systems is a special case of the new type of conserved quantity given in this paper.     

Mei Symmetry and Lie Symmetry of Relativistic Hamiltonian System

The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained.An example is given to illustrate the application of the result.     

A New Type of Mei Adiabatic Invariant Induced by Perturbation to Mei Symmetry of Hamiltonian Systems

Considering full perturbation to infinitesimal generators in the Mei structure equation, a new type of Mei adiabatic invariant induced by perturbation to Mei symmetry for Hamiltonian system was reported.     

Lie symmetry and Mei conservation law of continuum system

Lie symmetry and Mei conservation law of continuum Lagrange system are studied in this paper.The equation of motion of continuum system is established by using variational principle of continuous coordinates.The invariance of the equation of motion under an infinitesimal transformation group is determined to be Lie-symmetric.The condition of obtaining Mei conservation theorem from Lie symmetry is also presented.An example is discussed for applications of the results.     

A New Type of Mei Adiabatic Invariant Induced by Perturbation to Mei Symmetry of Hamiltonian Systems

Considering full perturbation to infinitesimal generators in the Mei structure equation, a new type of Mei adiabatic invariant induced by perturbation to Mei symmetry for Hamiltonian system was reported.     

广义经典力学系统的对称性与Mei守恒量

研究广义经典力学系统的对称性和一类新型守恒量——Mei守恒量.在高维增广相空间中建立 了系统的运动微分方程；给出了系统的Mei对称性、Noether对称性和Lie对称性的判据；得 到了分别由三种对称性导致Mei守恒量的条件和Mei守恒量的形式.举例说明结果的应用. 关键词： 广义经典力学 Mei对称性 Noether对称性 Lie对称性 守恒量     

Two New Types of Conserved Quantities of Mei Symmetry for Holonomic Mechanical System

Two new types of conserved quantities directly deduced by Mei symmetry of holonomic mechanical system are studied. The definition and criterion of Mei symmetry for holonomic system are given. A coordination function is introduced, the conditions under which the Mei symmetry can directly lead 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 result indicates that the coordination function can be selected properly according to the demand of the gauge function, thereby the gauge function can be found out more easily. Furthermore, since the choice of the coordination function has multiformity, much T more conserved quantity of Mei symmetry for holonomic mechanical system can be obtained.     

Mei Symmetry and Lie Symmetry of Relativistic Hamiltonian System

The Mei symmetry and the Lie symmetry of the relativistic Hamiltonian system are studied. The definition and criterion of the Mei symmetry and the Lie symmetry of the reoativistic Hamiltonian system are given. The relationship between them is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.     

A New Type of Conserved Quantity Deduced from Mei Symmetry for Relativistic Mechanical System in Phase Space

In this paper, a new type of conserved quantity indirectly deduced from the Mei symmetry for relativistic mechanical system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The condition for existence and the form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the results.     

Mei Symmetry and Lie Symmetry of the Rotational Relativistic Variable Mass System

The Mei symmetry and the Lie symmetry of a rotational relativistic variable masssystem are studied. Thedefinitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system aregiven. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Meisymmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.     

Mei Symmetry and Noether Symmetry of the Relativistic Variable Mass System

The definition and criterion of the Mei symmetry of a relativistic variable mass system are given. The relation between the Mei symmetry and the Noether symmetry of the system is found under infinitesimal transformations of groups. The conserved quantities to which the Mei symmetry and Noether symmetry of the system lead are obtained. An example is given to illustrate the application of the result.     

Mei Symmetry and Lie Symmetry of the Rotational Relativistic Variable Mass System

The Mei symmetry and the Lie symmetry of a rotational relativistic variable mass system are studied. The definitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system are given. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.     

Integrating Factors and Conservation Theorems of Lagrangian Equations for Nonconservative Mechanical System in Generalized Classical Mechanics

The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.     

Integrating Factors and Conservation Theorems of Lagrangian Equations for Nonconservative Mechanical System in Generalized Classical Mechanics

The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.