变质量单面非完整系统的Lie对称性与守恒量

LIE SYMMETRIES AND CONSERVED QUANTITIES OF NONHOLONOMIC SYSTEMS HAVING VARIABLE MASS AND UNILATERAL CONSTRAINTS

本文首先利用微分方程在无限小群变换下的不变性建立了变质量单面非完整系统的Lie对称性的确定方程和限制方程 ,给出了系统的结构方程和守恒量 ;其次讨论了系统的Lie对称性的逆问题 ;最后举例说明结果的应用。

The paper establishes the determining and restriction equations of Lie symmetries for nonholonomic systems of variable mass with unilateral constraints It gives the structural equation and the conserved quantities, using the invariancy of ordinary differential equations under infinitesimal transformations The paper also studies the inverse problem of Lie symmetries Applications of the results are given by an example