Determine the eigenvalues and eigenvectors of A. Radiation from a System of Uniformly Circling Charges

Recently it has been shown by numerical calculations that the power radiated by a classical system of two particles of equal (like or unlike) charge and mass, which orbit uniformly and diametrically opposite each other on a circle, equals the rate at which work is done on the particles against their retarded electromagnetic interactions and the Lorentz-Dirac radiation reaction forces. Thus, it has been demonstrated numerically that, contrary to a previous claim [2], the Lorentz-Dirac equation and the retarded Lienard-Wiechert potentials of classical electrodynamics satisfy energy conservation in such systems. The total power P radiated by such a system can be calculated using Fourier series methods, and is given exactly [3] b