Stabilization of an Euler-Lagrange system onto a constraint surface when the system makes contact with a nonzero impact velocity is an important problem in systems interacting with external environments. Potential applications include robotic surface following and surface finishing operations in manufacturing industry. In this paper, the constrained dynamic equations are modeled as a set of nonsmooth differential equations depending on whether the system lies on the constraint surface or the system repeatedly makes and loses contact with the constraint surface. The focus is on the initial condition problem, i.e., the system hits the constraint with a nonzero impact velocity. A new discontinuous control scheme is proposed that ensures stable regulation of the system onto the constraint surface.