Symmetries and Two Types of Non-Noether Conservation Laws of Birkhoffian System with Unilateral Constraints

The symmetries and non-Noether conservation laws ofBirkhoffian system with unilateral constraints are studied. Thedifferential equations of motion of the system are established,and the criterions of Noether symmetry, Lie symmetry and Meisymmetry of the system are given. Two types of new conservationlaws, called the Hojman conservation law and the Mei conservationlaw respectively, are obtained, and the intrinsic relations amongthe symmetries and the new conservation laws are researched.At the end of the paper, an example is given to illustrate theapplication of the results.