Semiflexible polymers are often modelled as consisting of rigid segments connected by rigid rods, ball-socket joints or springs. In this paper we focus on polymers consisting of two identical segments connected by a frictionless ball-socket joint. This introduces rigid constraints, resulting in the number of degrees of freedom being reduced. Using kinetic theory we derive the effective hydrodynamic mobility tensor of each segment in the chain, expressed in terms of the hydrodynamic mobility of an identical free segment. The result is used to obtain analytical and numerical expressions for the slowest decay mode in a typical transient electrically induced birefringence experiment. We show that under typical experimental conditions only this single mode will be present. The results we obtain are significantly different from results for a similar once-broken rod published by Wegener and co-workers and Garcia de la Torre and co-workers. In the last part of the paper Brownian dynamics simulations of the two-segment model is used to verify our analytically obtained expressions for the mobility tensor and decay modes and to obtain results for situations where analytical results are unavailable. The model assumes no hydrodynamic interaction between the segments. (C) 2003 American Institute of Physics.