Abstract
In this paper, a new symmetry, i.e., Noether-Lie symmetry and its conserved quantities of the non-holonomic mechanical system is studied. The definition and the criterion of the Noether-Lie symmetry for the system are given. A theorem asserting that the Noether-Lie symmetry for the system leads to both the Noether conserved quantity and the general Hojman conserved quantity is presented. An example is given to illustrate the application of the result. The Hojman conserved quantity of the system is a special case of the general Hojman conserved quantity obtained in this paper.
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