A new approach to radiation reaction for the correction of the linear and circular motion of a charged particle takes into account the emission of electromagnetic radiation due to its acceleration. This new formulation was based on expressing the radiation reaction force in terms of the external force rather than the acceleration of the charge. In this paper, a generalization of the radiation reaction force in terms of the external force approach is formulated for any arbitrary motion of the charged particle. This generalization includes the linear and circular acceleration cases previously investigated.
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