  A number of new closed-form fundamental solutions for the generalized
unsteady Oseen and Stokes flows associated with arbitrary time-dependent
translational and rotational motions have been developed. These solutions are
decomposed into two parts corresponding to a longitudinal wave and a
transversal wave. As examples of application, the hydrodynamic force acting on
a sphere or on a circular cylinder translating in an unsteady flow field at low
Reynolds numbers are calculated using the new generalized fundamental
solutions. The results for a rotating viscous flow past an impulsively moving
sphere and an impulsively moving circular cylinder are entirely new.
