高维增广相空间中广义完整非保守力学系统的Lie对称定理及其逆定理

Lie symmetries theorem and its inyerse of generalized holonomic non-conservative dynamical systems in the high-dimensional extended phase space

依据广义增广相空间中完整非保守力学系统的运动微分方程在无限小变换下的不变性,建立系统的确定方程,给出结构方程和守恒量的形式及有关结论的逆命题。

By means of the invariance of the differential equation of motion under the infinitesimal transformations of holonomic non-conservative dynamical systems in the high-dimensional extended phase space. The determining equations of the Lie symmetries were established. The structure equation and the form of conserved quantities and some related propositions were obtained.