单面非Chetaev型非完整系统相对于非惯性系的Lie对称性与守恒量

LIE SYMMETRIES AND CONSERVED QUANTITIES OF NON-HOLONOMIC SYSTEMS OF NON-CHETAEV'S TYPE WITH UNILATERAL CONSTRAINTS RELATIVE TO A NON-INERTIAL REFERENCE FRAME

本文研究单面非 Chetaev型非完整系统相对于非惯性系的 Lie对称性与守恒量。首先利用微分方程在无限小变换下的不变性建立 Lie对称性所满足的确定方程和限制方程 ,给出结构方程和守恒量 ;其次讨论系统的 Lie对称逆问题 ;最后举例说明结果的应用。

This paper studies the Lie symmetries and conserved quantities of non holonomic systems of non Chetaev's type with unilateral constraints relative to a non inertial reference frame The invariance of ordinary differential equations under infinitesimal transformations is used to establish the determining equations and restrictions of the Lie symmetries of the systems The structural equation and conserved quantities are thus obtained The inverse problem of Lie symmetries is then discussed An example to illustrate the application of the results is finally given