变质量单面非Chetaev型非完整系统的Lie对称性与守恒量

LIE SYMMETRY AND CONSERVED QUANTITY OF NONHOLONOMIC SYSTEM OF NON-CHETAEV'S TYPE WITH UNILATERAL CONSTRAINTS OF VARIABLE MASS

利用微分方程在无限小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 ,并讨论了系统的Lie对称逆问题 ,给出了应用实例。

Lie symmetry and conserved quantity of nonholonomic system of no Chetaev's type are studied with unilateral constraints of variable mass. By using the invariance of the ordinary differential equations under the infinitesimal transformation, the determining equations and the restriction of the Lie symmetry of the system are established, and the structure equation and conserved equation are obtained. The inverse problem of Lie symmetry is discussed. An example is given to illustrate the application of the result.