  We analyze the dynamics of the shell produced when a bow shock from a
collimated jet propagates into the surrounding medium. Under interstellar
conditions, the shock is radiative, and a ballistic approximation for the shell
flow is appropriate beyond the working surface where the jet impacts its
surroundings. The solution is then determined by the ambient and jet densities
and velocities and by the momentum impulse applied in the working surface.
Using estimates for these impulses (confirmed by separate numerical
simulations), we obtain solutions for the shell structure, and for the range of
velocities in the shell at any point. We provide predictions for the
position-velocity and mass-velocity relations expected for plane-of-sky
bow-shock shells, and for the bulk shell properties. In a companion paper, we
show that these analytic solutions are in excellent agreement with the results
of direct numerical simulations. We argue that classical molecular (CO)
outflows cannot be purely jet-driven, because the bow-shock shell solutions are
much too elongated compared with observations. Finally, we suggest that the
``spur'' structures seen in position-velocity diagrams of observed molecular
outflows are the manifestation of internal bow shocks which may be fit with our
simple dynamical models.
