This dissertation provides a complete mathematical framework to compute the sensitivities with respect to system parameters for any second order hybrid Ordinary Di erential Equation (ODE) and rank 1 and 3 Di erential Algebraic Equation (DAE) systems. The hybrid system is characterized by discontinuities in the velocity state variables due to an impulsive forces at the time of event. At the time of event, such system may also exhibit a change in the equations of motion or in the kinematicâ€¦Â Expand