  We study the three-dimensional dynamics of a spherical microswimmer in
cylindrical Poiseuille flow which can be mapped onto a Hamiltonian system.
Swinging and tumbling trajectories are identified. In 2D they are equivalent to
oscillating and circling solutions of a mathematical pendulum. Hydrodynamic
interactions between the swimmer and confining channel walls lead to
dissipative dynamics and result in stable trajectories, different for pullers
and pushers. We demonstrate this behavior in the dipole approximation of the
swimmer and with simulations using the method of multi-particle collision
dynamics.
