  A new solution method is presented for steady-state, momentum-conserving,
non-axisymmetric bow shocks and colliding winds in the thin-shell limit. This
is a generalization of previous formulations to include a density gradient in
the pre-shock ambient medium, as well as anisotropy in the pre-shock wind. For
cases where the wind is unaccelerated, the formalism yields exact, analytic
solutions.
  Solutions are presented for two bow shock cases: (1) that due to a star
moving supersonically with respect to an ambient medium with a density gradient
perpendicular to the stellar velocity, and (2) that due to a star with a
misaligned, axisymmetric wind moving in a uniform medium. It is also shown
under quite general circumstances that the total rate of energy thermalization
in the bow shock is independent of the details of the wind asymmetry, including
the orientation of the non-axisymmetric driving wind, provided the wind is
non-accelerating and point-symmetric. A typical feature of the solutions is
that the region near the standoff point is tilted, so that the star does not
lie along the bisector of a parabolic fit to the standoff region. The principal
use of this work is to infer the origin of bow shock asymmetries, whether due
to the wind or ambient medium, or both.
