Discontinuous trajectories of Lagrangian systems with singular hypersurface

It is shown that a Lagrangian system whose Legendre transformation degenera tes along a hypersurface behaves in a strange manner by jumping from time t o time without any "visible cause." In such a jump the system changes insta ntaneously its coordinates as well as its momenta. Necessary elements of th e general theory of such systems are reported and a detailed description of a postrelativistic oscillator showing such a behavior is given. (C) 2001 A merican Institute of Physics.