  Circumstellar dust particles can be captured in a mean motion resonance with
a planet and simultaneously be affected by non-gravitational effects. It is
possible to describe the secular variations of a particle orbit in the mean
motion resonance analytically using averaged resonant equations. We derive the
averaged resonant equations from the equations of motion in near-canonical
form. The secular variations of the particle orbit depending on the orientation
of the orbit in space are taken into account. The averaged resonant equations
can be derived/confirmed also from Lagrange's planetary equations. We apply the
derived theory to the case when the non-gravitational effects are the
Poynting--Robertson effect, the radial stellar wind, and an interstellar wind.
The analytical and numerical results obtained are in excellent agreement. We
found that the types of orbits correspond to libration centers of the
conservative problem. The averaged resonant equations can lead to a system of
equations which hold for stationary points in a subset of resonant variables.
Using this system we show analytically that for the considered
non-gravitational effects, all stationary points should correspond to orbits
which are stationary in interplanetary space after an averaging over a synodic
period. In an exact resonance, the stationary orbits are stable. The stability
is achieved by a periodic repetition of the evolution during the synodic
period. Numerical solutions of this system show that there are no stationary
orbits for either the exact or non-exact resonances.
