This study presents a novel approach for evaluating the effects of dynamic disturbances on optical performance using sensitivity analysis. The computation of optical performance for perturbed optical systems is too costly with state-of-the-art analysis software when applied in the use case for the optimization of the optomechanical interface, and therefore using a simplified model, based on ray transfer matrices, describing the most critical phenomena provides a solution. The proposed analytical framework employs a Taylor expansion for the merit function, incorporating both the Jacobian and Hessian matrices, to reduce computation time in transient analysis. The effect of small perturbations on the merit function is found to be accurately described by the approximation when solely the Jacobian is included, for larger displacement fields the approximation deviates significantly without the inclusion of the Hessian. Next to this, the definition of a grating matrix is appended to the framework to facilitate the analysis of a larger set of systems. For transient analysis, the proposed framework exhibits a remarkable improvement in computation time, with minimal degradation in accuracy for paraxial systems. All findings hold relevance for the effect of rigid body displacements in coupled mechanical-optical analyses and further optimization of this coupling under disturbed conditions.