This paper studies the symmetries and the conserved quantities for systems with unilateral holonomic constraints. The definitions of Lie symmetries for the systems are given, and the Lutzky conserved quantities are directly deduced from the general velocity-dependent Lie symmetries of the systems. The Lutzky conserved quantities of some special cases, for example, the holonomic systems with remainder coordinetes, the non-conservative mechanical systems, and the Lagrangian systems, are given. At the end of the paper, two examples are given to illustrate the application of the results.
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