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中文摘要：
介绍了对Lagrange系统Noether对称性的两种理解，一种理解为Lagrange函数的不变性，另一种理解为作用量的不变性．研究表明，这两种理解是不同的．在一些条件下，Lagrange函数的不变性可以成为作用量的不变性，在另一些条件下，作用量的不变性可以成为Lagrange函数的不变性．将Noether对称性理解为作用量的不变性是合理的．
英文摘要：
This paper presents two ways of comprehending the Noether symmetry for the Lagrange system. One is based on invariance of the Lagrangian, the other is based on invariance of the action. This paper proves that these two comprehensions are different from each other. We give the condition under which the invariance of the Lagrangian can become the invariance of the action,and the condition under which the invariance of the action can become the invariance of the Lagrangian is obtained. It is suitable that the Noether symmetry is comprehended as the invariance of the action.
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