  This paper provides an analytical methodology to compute the sensitivities
with respect to system parameters for any second order hybrid Ordinary
Differential Equation (ODE) system. The hybrid ODE system is characterized by
discontinuities in the velocity state variables due to an impulsive jump caused
by an instantaneous impact in the motion of the system. The analytical
methodology that solves this problem is structured based on jumping conditions
for both the state variables and the sensitivities matrix. The proposed
analytical approach is of the benchmarked against a numerical method.
