Second order systems whose drift is defined by the gradient of a given potential are considered, and minimization of the L-1-norm of the control is addressed. An analysis of the extremal flow emphasizes the role of singular trajectories of order two [H. M. Robbins, AIAA J., 3 (1965), pp. 1094-1098; M. I. Zelikin and V. F. Borisov, Theory of Chattering Control, Birkhauser, Basel, 1994]; the case of the two-body potential is treated in detail. In L-1-minimization, regular extremals are associated with controls whose norm is bang-bang; in order to assess their optimality properties, sufficient conditions are given for broken extremals and related to the no-fold conditions of [J. Noble and H. Schattler, J. Math. Anal. Appl., 269 (2002), pp. 98-128]. Two examples of numerical verification of these conditions are proposed on a problem coming from space mechanics.