Applications of the Lorentz-Abraham-Dirac equation in long-term dynamics

To improve the presentation we modified the title and used the framework of perturbation modeling of long-term dynamics so as to present the Lorentz-Abraham-Dirac equation as the lowest order, asymptotic differential relation for the velocity of a charged point-like mass. We formulated two propositions and added two references.
Comment: PACS numbers: 03.50.De; 45.50.-j; 11.30.-j; 29.20.-c; 45.05.+x Keywords: Radiation-reaction force, particle trajectory; accelerators. arXiv admin note: substantial text overlap with arXiv:1005.3943