This paper presents a constrained theory for smectic C liquid crystals that may be useful for the analysis of some effects in these materials. The theory is based on two simplifying assumptions, namely that the layers although deformed remain of constant thickness, and also that the tilt with respect to the layer normal remains fixed. The equilibrium version of the theory proves to be a non-linear generalization of the earlier Orsay theory, and promises to model a number of static effects satisfactorily. Here our aim is to examine preliminary predictions based on the corresponding dynamic theory, where some progress proves possible for shear flow, and also for a shear wave reflection-refraction experiment useful for the measurement of some viscous coefficients.