  The dynamics of phantom bead-spring chains with the topology of a symmetric
star with $f$ arms and tadpoles ($f=3$, a special case) is studied, in the
overdamped limit. In the simplified case where the hydrodynamic radius of the
central monomer is $f$ times as heavy as the other beads, we determine their
dynamical eigenmodes exactly, along the lines of the Rouse modes for linear
bead-spring chains. These eigenmodes allow full analytical calculations of
virtually any dynamical quantity. As examples we determine the radius of
gyration, the mean square displacement of a tagged monomer, and, for star
polymers, the autocorrelation function of the vector that spans from the center
of the star to a bead on one of the arms.
