一阶Lagrange系统的Lie对称性与守恒量

LIE SYMMETRIES AND CONSERVED QUANTITIES OF FIRST ORDER LAGRANGE SYSTEMS

将一阶微分方程组化成一阶Lagrange方程 .利用常微分方程在无限小变换下的不变性 ,建立Lie对称性的确定方程 .给出Lie对称性导致守恒量的条件以及守恒量的形式 .

In this paper, a system of first order ordinary differential equations is expressed in the form of first order Lagrange equations. The determining equations of Lie symmetries are established by the invariance of the ordinary differential equations under the infinitesimal transformations. The condition under which a Lie symmetry can lead to a conserved quantity is obtained and the form of the conserved quantities is given.