The Vlasov technique is used to model the electron cooling force. Limitations of the applicability of the method is obtained by considering the perturbations of the electron plasma. Analytical expressions of the electron cooling force, valid beyond the Coulomb logarithm approximation, are derived and compared to numerical calculations using adaptive Monte Carlo integration. The calculated longitudinal cooling force is verified with measurements in CELSIUS. Transverse damping rates of betatron oscillations for a nonlinear cooling force is explored. Experimental data of the transverse monochromatic instability is used to determine the rms angular spread due to solenoid field imperfections in CELSIUS. The result, θrms= 0.16 ± 0.02 mrad, is in agreement with the longitudinal cooling force measurements. This verifies the internal consistency of the model and shows that the transverse and longitudinal cooling force components have different velocity dependences. Simulations of electron cooling with applications to HESR show that the momentum reso- lution ∆p/p smaller than 10−5 is feasible, as needed for the charmonium spectroscopy in the experimental program of PANDA. By deflecting the electron beam angle to make use of the monochromatic instability, a reasonable overlap between the circulating antiproton beam and the internal target can be maintained. The simulations also indicate that the cooling time is considerably shorter than expected.