Lie symmetries of mechanical systems with unilateral holonomic constraints

In the recent twenty years, the study on the Lie symmetries and conserved quantities of constrained mechanical systems has been making great progress[1-5]. Up to now, however, all the studies are limited to the mechanical systems with ideal bilateral constraints. This note further studies the Lie symmetries of mechanical systems with unilateral holonomic constraints, and two problems of Lie symmetries for the systems are put forward and solved, i.e. finding the conserved quantity from a Lie symmetric transformation of the system and finding the corresponding Liesymmetry from an integral of the systemi ? 梛 ? Jsymmetry from an integral of the system.