Transient waves produced by a moving source on a circle

The goal of the present paper is to obtain the solutions of the initial-value problem to the inhomogeneous wave and Maxwell´s equations in the space-time domain. We suppose that the point source starts at the fixed moment of time and moves with arbitrary velocity on a circle. General expressions obtained previously enable us to give a description of the wavefunctions and components of the vector potential in terms of the transient modes in a cylindrical coordinate system. Eventually, we represent the obtained expansions in terms of the Fourier series, whose coefficients are explicit functions of the space-time variables. Due to the property of the delta-function, we manage to sum up the series. We apply the obtained expressions to the description of waves in the particular case of a point source moving with a constant angular velocity and give the relations, which characterize both transient and steady-state waves. We define the space-time domain where the steady-state waves exist