Hyper-impulsive motion on manifolds

Hyper-impulsive motion is a branch of control theory applied to Lagrangian mechanical systems developed in [8]. Suppose that part of system's coordinates are 'controllized' i.e. identified with a control function u that can be discontinuous. Due to the presence of the derivative of u in the dynamic equation, the resulting motion is discontinuous both in the configurations and momenta in the general case. In this paper we show that the discontinuity in the phase-space trajectory consequent to a jump (a finite discontinuity) of the control can be determined by a parallel transport operation relatively to the dynamic connection introduced by C.M. Marle