Symmetries And Non-Noether Conserved Quntities Of Systems With Unilateral Constraints

The researches on the symmetry theory and the conservation laws of mechanical systems have important theoretical and practical significance. The modern methods to find conserved quantities are the followings: Noether symmetry,Lie symmetry and Mei symmetry. In the paper, we study the unified symmetry of mechanical systems of unilateral holonomic constraints with remainder coordinates,holonomic systems with variable mass and unilateral constraints,holonomic systems of unilateral constraints in phase space,systems with unilateral Chetaev non-holonomic constraints,systems with unilateral non-Chetaev non-holonomic constraints,systems with unilateral Vacco constraints, the definition and criterions of Noether symmetry,Lie symmetry and Mei symmetry for the systems are presented, the criterion of unified symmetry are found, the condition and the form of two type of non-Noether conserved quantities :the general Hojman conserved quantity and the Mei conserved quantity are given due to the unified symmetry of the systems. At last, under the condition of unilateral constraints, the symmetry and conserved quantity of the singular system is studied, the unifed symmetry of non-holonomic singular system and non-holonomic singular system with unilateral constraints are studied, the condition and the form of two type of non-Noether conserved quantities: the general Hojman conserved quantity and the Mei conserved quantity are given due to the unified symmetry of the systems.