Simplified models of electromagnetic and gravitational radiation damping

In previous work the authors have analysed the global properties of an appr oximate model of radiation damping for charged particles. This work is put into context and related to the original motivation of understanding approx imations used in the study of gravitational radiation damping. We examine t o what extent the results obtained previously depend on the particular mode l chosen. Comparisons are made with other models for gravitational and elec tromagnetic fields. The relation of the kinetic model for which theorems we re proved to certain many-particle models with radiation damping is exhibit ed.