Conformal invariance and conserved quantities of mechanical system with unilateral constraints

By distinguishing the different constraint cases, the whole course and piecewise conserved quantities, which deduced from conformal invariance of mechanical systems with unilateral constraints, are given. The determining equation of conformal invariance of the system is obtained. The sufficient and necessary conditions for the conformal invariance must be Lie symmetry of the system are given. The forms of conformal factors are obtained. An example is given to illustrate the results in this paper.