Mei symmetry of Tzénoff equations of holonomic system

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.     

Unified Symmetry of Nonholonomic Mechanical Systems with Non-Chetaev＇s Type Constraints

Based on the total time derivative along the trajectory of the system, the unified symmetry of nonholonomic mechanical system with non-Chetaev＇s type constraints is studied. The definition and criterion of the unified symmetry of nonholonomic mechanical systems with non-Ohetaev＇s type constraints are given. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, is obtained. Two examples are given to illustrate the application of the results.     

Two Types of New Conserved Quantities and Mei Symmetry of Mechanical Systems in Phase Space

In this paper, two types of new conserved quantities directly deduced by Mei symmetry in phase space are studied. The conditions under which Mei symmetry can directly lead to the two types of new conserved quantities and the forms of the two types of new conserved quantities are given. An example is given to illustrate the application of the results.     

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in phase space are presented. The definition and the criterion for this system are presented. A new conserved quantity and the Noether conserved quantity deduced from the Noether-form invariance are obtained. An example is given to illustrate the application of the results.     

On Form Invariance,Lie Symmetry,and Three Kinds of Conserved Quantities of Generalized Lagrange's Equations

In this paper, the form invariance and the Lie symmetry of Lagrange's equations for nonconservative system in generalized classical mechanics under the infinitesimal transformations of group are studied, and the Noether's conserved quantity, the new form conserved quantity, and the Hojman's conserved quantity of system are derived from them. Finally, an example is given to illustrate the application of the result.     

A series of non-Noether conservative quantities and Mei symmetries of nonconservative systems

In this paper Mei symmetry is introduced for a nonconservative system. The necessary and sufficient condition for a Mei symmetry to be also a Lie symmetry is derived. It is proved that the Mei symmetry leads to a non-Noether conservative quantity via a Lie symmetry, and deduces a Lutzky conservative quantity via a Lie point symmetry.     

时变垂向入渗影响下河渠-潜水非稳定渗流模型的解及应用

在河渠边界控制下的半无限含水层中,对时变垂向入渗影响下的潜水非稳定渗流模型,利用Boussinesq第一线性化方法,通过Laplace变换并结合卷积原理,导出模型的解析解．根据不同水文地质条件下解的数学特征,建立相应的含水层参数求解方法;在此基础上,建立计算河渠与含水层之间水量交换的公式,以及计算潜水蒸发强度的递推公式．以安徽淮北平原某河流-潜水含水层系统为例,阐述上述方法的计算过程与步骤．     

Non-Noether Conserved Quantity of Nonholonomic System Having Variable Mass and Unilateral Constraints

Using the Lie Symmetry under infinitesimal transformations in which the time is not variable, the nonNoether conserved quantity of nonholonomic system having variable mass and unilateral constraints is studied. The differential equations of motion of the system are given. The determining equations of Lie symmetrical transformations of the system under infinitesimal transformations are constructed. The Hojman‘s conservation theorem of the system is established. Finally, we give an example 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.     

A new conserved quantity of mechanical systems with differential constraints

A new conserved quantity of non-Noether symmetry for the mechanical systems with differential constraints is studied. First, the differential equations of motion of the systems are established. Then, the determining equations and restriction equations of the non-Noether symmetry are obtained and a new conserved quantity is given. Finally, an example is given to illustrate the application of the results.