关于由拉格朗日方程得到能量积分的条件

On the Condition of Obtaining Energy Integral from Lagrange Equations

由拉格朗日方程得到能量积分的条件常常被表述为体系所受约束为稳定约束。本文以具体例子清楚地指明，由拉格朗日方程能否得到能量积分，这与体系所受约束是否是稳定约束并无确定的联系：在体系所受约束为不稳定约束的情况下，由拉格朗日方程也可能得到能量积分；而在约束为稳定约束的情况下却未必能得到能量积分．

The condition of obtaining energy integral from lagrange equations is usullyconsidered to be that the constraints restricting the considered system are stable. By the useof some examples ,it is clearly pointed ont in this paper that this view is nut right。In the casethat the constraints are unstable it is possible that energy integrals are obtained from Lagrange equations,but in the case that the constraints are stable it cowld not be ensured.