Form invariance and Lie symmetry of equations of non-holonomic systems

In this paper, we study the relation between the form invariance and Lie symmetry of non-holonomic systems. Firstly, we give the definitions and criteria of the form invariance and Lie symmetry in the systems. Next, their relation is deduced. We show that the structure equation and conserved quantity of the form invariance and Lie symmetry of non-holonomic systems have the same form. Finally, we give an example to illustrate the application of the result.