非Chetaev型非完整系统相对非惯性系的Lie对称性与守恒量

LIE SYSMMETRIES AND CONSERVED QUANTITIES OF NONHOLONOMIC SYSTEMS OF NON CHETAEV’S TYPE RELATIVE TO NON INERTIAL REFERCE FRAME

研究非Ｃｈｅｔａｅｖ 型非完整系统相对非惯性系的Ｌｉｅ 对称性与守恒量．首先，利用微分方程在无限小群变换下的不变性建立了Ｌｉｅ 对称性所满足的确定方程，给出了结构方程和守恒量；其次讨论了系统的Ｌｉｅ 对称逆问题；

The study of conservation laws of dynamical system is a significant aspect of modern analytical mechanics.There are two kinds of modern methods in finding conservation laws.One is the Noether method which is based on the invariance of the Hamilton's action under the infinitesimal transformations,other one is the Lie method which is based on the invariance of the differential equations under infinitesimal transformations.This paper study Lie symmetries and conserved quantities of nonholonomic systems of non Chetaev's type relative to non inertial reference frame.Firstly,it establishes the determining equations and the restriction equations of the Lie symmetries and it gives the structure equation and the conserved quantities,which are using the invariance of the ordinary differential equations under the infinitesimal transformations.Secondly,it studies the inverse problem of Lie symmetries of the systems.Finally,it gives an example to illustrate the application of the result.Since Cheteav's nonholonomic system is a special case of the non Cheteav's type and it studies relative to non inertial reference frame,the results in this paper have more universality.