  Typically the motion of self-propelled active particles is described in a
quiescent environment establishing an inertial frame of reference. Here we
assume that friction, self-propulsion and uctuations occur relative to a
non-inertial frame and thereby the active Brownian motion model is generalized
to non-inertial frames. First, analytical solutions are presented for the
overdamped case, both for linear swimmers and circle swimmers. For a frame
rotating with constant angular velocity ("carousel"), the resulting noise-free
trajectories in the static laboratory frame trochoids if these are circles in
the rotating frame. For systems governed by inertia, such as vibrated
granulates or active complex plasmas, centrifugal and Coriolis forces become
relevant. For both linear and circling self-propulsion, these forces lead to
out-spiraling trajectories which for long times approach a spira mirabilis.
This implies that a self-propelled particle will typically leave a rotating
carousel. A navigation strategy is proposed to avoid this expulsion, by
adjusting the self-propulsion direction at wish. For a particle, initially
quiescent in the rotating frame, it is shown that this strategy only works if
the initial distance to the rotation centre is smaller than a critical radius
Rc which scales with the self-propulsion velocity. Possible experiments to
verify the theoretical predictions are discussed.
