  For problems with multiple bodies, the current integral approach needs the
use of auxiliary potential functions in order to have an individual force
formula for each body. While the singularity approach, based on an extension of
the unsteady Lagally theorem, is restricted to multibody and multivortex flows
without bound vortex and vortex production. In this paper, we consider
multibody and multivortex flow and derive force formulas, in both forms of
singularity approach and integral approach but without auxiliary function, that
give individual forces of each body for unsteady two dimensional potential flow
with vortex production on the surface of bodies. A number of problems,
including Karman vortex street, Wagner problem of impulsively starting flow,
interaction of two circular cylinders with circulation, and interaction of an
airfoil with a bound vortex, are used to validate the force formulas.
