相对论性变质量非完整可控力学系统的非Noether守恒量

Non-Noether conserved quantity for relativistic nonholonomic controllable mechanical system with variable mass

在时间不变的特殊无限小变换下,研究相对论性变质量非完整可控力学系统的非Noether守恒量——Hojamn守恒量.建立了系统的运动微分方程,给出了系统在特殊无限小变换下的形式不变性(Mei对称性)的定义和判据以及系统的形式不变性是Lie对称性的充分必要条件.得到了系统形式不变性导致非Noether守恒量的条件和具体形式.举例说明结果的应用.

The non-Noether conserved quantity for relativistic nonholonomic controllable mechanical system with variable mass is discussed under special infinitesimal transformations in which the time is not a variable.The differential equations of motion of the system are established.The definition and criterion of the form invariance of the system under special infinitesimal transformations are discussed.The necessary and sufficient conditions under which the form invariance is a Lie symmetry is presented.The conditions under which a non-Noether conserved quantity can be induced by the form invariance and the form of the conserved quantity are obtained.An example is presented to illustrate the application of the result.