  We study cylindrically symmetric steady-state accretion of polytropic test
matter spiraling onto the symmetry axis in power-law and logarithmic
potentials. The model allows one to qualitatively understand the accretion
process in a symmetry different from that of the classical Bondi accretion. We
study the integral curves as level lines of some Hamiltonian and also apply
this method to Bondi accretion. The isothermal solutions in power-law
potentials (as well as in any radius-dependent potential) can be expressed in
exact form in terms of the Lambert W function, while in the case of logarithmic
potential, exact solutions can be found for any polytropic exponent.
