  The fundamentals of Brownian motion have been largely well understood since
the early 20th century, with most recent additions focusing on understanding
anomalous diffusion via rescaling of drag coefficents. That focus emphasizes
long-time dynamic behavior, but recent results indicate that additional,
secondary modes are also present at short and intermediate times in fluids of
anisotropic particles. Here, we study the dynamics of a representative family
of nearly-hard n-gons. Using molecular dynamics simulations, we study a
distinct form of caging only present in anisotropic systems. We show that this
caging behavior emerges in the mean squared displacement of n-gons at
intermediate particle volume fractions. We then develop an extended Langevin
theory directly coupling translational and rotational motion as a function of
the relative anisotropy for different n-gons that predicts the observed caging
behavior. Extending our theory to incorporate secondary, off-phase
cross-correlations between particles further enables the prediction of both
translational and rotational relaxation times of the system.
