Rc. Zhang et al., Effects of nonholonomic constraint on Lie symmetries and conserved quantities of Lagrangian systems, CHIN PHYS, 9(8), 2000, pp. 561-564
After a Lagrangian system is constrained by nonholonomic constraints, the d
etermining equations, the structure equation and the form of conserved quan
tities corresponding to the Lie symmetries will change. Some symmetries van
ish and under certain conditions some Lie symmetries still remain.