In this article, we establish the validity of a relation between the true angular velocity and gyration tensor for a dilute polymer solution in the case of a steady shear flow by means of nonequilibrium molecular dynamics computer simulation. The microscopic model for a polymer molecule immersed in a solution composed of monomers incorporates the effects of hydrodynamic interaction through the presence of explicit solvent monomers and the effect of finite stretchability of chains. In the strong flow regime, we observe regular and irregular dynamical behavior which is inherently connected with the nonlinearities. in the equations of motion which come along with finite extendability of polymer chains. The microscopic dynamics underlying the simple relationship, and in particular the time series, the correlated rotation and deformation behavior, and cross-correlations between several structural quantities are investigated in detail. The results allow for a test of more efficient implementations, which aim to describe polymer dynamics considering hydrodynamic interactions by using ad hoc Langevin equations for the conformational variables.