Stability analysis of driver’s two-body electrodynamics model

An analysis of the stability of the two-body electrodynamic model proposed by Driver is presented. The model incorporates retardation effects due to the finite propagation speed of electromagnetic interaction, resulting in delay-differential equations with state-dependent delays that govern the particles’ interactions and dynamics. We investigate the model stability in one-dimensional space under varying conditions. The analysis shows that the system cannot be linearized around an equilibrium point in the absence of an external field, owing to contradictory conditions. However, in the presence of an external field, the system possesses critical states around which the linear stability of the system can be analyzed. It is found that the system is generally unstable for any strength of the external field or separation between the two charges. The findings provide important insights into the role of retardation and external fields in the Driver’s classical electrodynamic model.