相对论性变质量系统积分不变量的构造

给出相对论性变质量非完整系统的非等时变分方程 ,并由第一积分构造了该系统积分不变量 。

相对论性变质量系统的Lie对称性与守恒量

给出相对论性变质量系统的正则方程 ,利用其在无限小变换下的不变性条件 ,建立相对论性变质量系统的Lie对称性确定方程 ,得到结构方程和守恒量。

转动相对论性变质量系统的广义Noether定理

研究转动相对论性变质量系统的广义Noether定理 ,首先给出转动相对论性变质量非完整系统的Lagrange方程 ;其次利用Hamilton作用量在无限小变换下的不变性 ,研究了转动相对论性变质量非完整系统的广义Noether定理和转动相对论性变质量非完整系统的广义Noether逆定理 ;结论具有普遍意义 ,对于经典情形和相对论情形都适用 ,若moi为常量 ,结果化为转动相对论性常质量的Noether定理 ;若 θi Γi,ωi Γi,结果化为经典转动变质量系统的Noether定理 ;若为常量 ,且 θ Γi,ωi Γi,则结果化为经典转动常质量系统的Noether定理。

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.

Non-Noether Conserved Quantity for Relativistic Nonholonomic System with Variable Mass

Using form invariance under special infinitesimal transformations in which time is not variable, the non-Noether conserved quantity of the relativistic nonholonomic system with variable mass is studied. The differential equations of motion of the system are established. The definition and criterion of the form invariance of the system under infinitesimal transformations are studied. The necessary and sufficient. condition under which the form invariance is a Lie symmetry is given. The condition under which the form invariance can be led to a non-Noether. conserved quantity and the form of the conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

A New Type of Conserved Quantity of Mei Symmetry for Relativistic Variable Mass Mechanical System in Phase Space

In this paper, a new type of conserved quantity directly deduced from the Mei symmetry for relativistic variable mass system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions 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 Symmetries and Lie Symmetries for Nonholonomic Controllable Mechanical Systems with Relativistic Rotational Variable Mass

The Mei symmetries and the Lie symmetries for nonholonomic controllable mechanical systems with relativistic rotational variable mass are studied. The differential equations of motion of the systems are established. The definition and criterion of the Mei symmetries and the Lie symmetries of the system are studied respectively. The necessary and sufficient condition under which the Mei symmetry is Lie symmetry is given. The condition under which the Mei symmetries can be led to a new kind of conserved quantity and the form of the conserved quantity are obtained. An example is given to illustrate the application of the results.

A Unified Symmetry of Mechanical Systems with Variable Mass in Phase Space

In this paper, the definition and the criterion of a unified symmetry of the mechanical system with variable mass in phase space are given. The Noether conserved quantity, the generalized Hojman conserved quantity, and Mei conserved quantity deduced from the unified symmetry are obtained. An example is given to illustrate the application of the results.