  A rigorous derivation and validation for linear fluid-structure-interaction
(FSI) equations for a rigid-body-motion problem is performed in an Eulerian
framework. We show that the added-stiffness terms arising in the formulation of
Fanion et al. (2000) vanish at the FSI interface in a first-order
approximation. Several numerical tests with rigid-body motion are performed to
show the validity of the derived formulation by comparing the time evolution
between the linear and non-linear equations when the base flow is perturbed by
identical small-amplitude perturbations. In all cases both the growth rate and
angular frequency of the instability matches within $0.1\%$ accuracy. The
derived formulation is used to investigate the phenomenon of symmetry breaking
for a rotating cylinder with an attached splitter-plate. The results show that
the onset of symmetry breaking can be explained by the existence of a
zero-frequency linearly unstable mode of the coupled
fluid-structure-interaction system. Finally, the structural sensitivity of the
least stable eigenvalue is studied for an oscillating cylinder, which is found
to change significantly when the fluid and structural frequencies are close to
resonance.
