Symmetries and conserved quantities of mechanical systems with unilateral holonomic constraints in phase space

The symmetries and conserved quantities of mechanical systems with unilateral holonomic constraints in extended phase space is studied. The differential equations of motion of the systems are established. The criterions of Noether symmetry, Lie symmetry and Mei symmetry are given, and the relations between the symmetries are researched. The Noether conserved quantity and two types of new conserved quantities, called the Hojman quantity and Mei quantity, for the systems are obtained, and intrinsic relations between the three symmetries and three types of conserved quantities are researched. An example is given to illustrate the application of the results.