Electromagnetic Scattering of Uniformly Moving PEC Objects—Part I: Integral Equation Formulations

A novel method is proposed for analyzing the electromagnetic scattering by an arbitrarily shaped perfectly electrically conducting (PEC) object in uniform motion in the vacuum. In Part I, the jump boundary conditions and the current continuity relation are simplified for PEC objects. A set of time-domain electromagnetic field integral equations on the surface of the moving PEC objects are formulated based on the jump boundary conditions. The relativity effect is properly addressed with the kinematic theorems. The hyper singularities associated with the Green’s function are analyzed and properly treated. The electromagnetic scattered fields generated by the induced current are determined according to the theory of special relativity (TSR) and the causality principle. All calculations are performed in the laboratory frame without explicitly applying Lorentz transformations. Consequently, it is also valid for analyzing systems including multiple objects uniformly moving with different velocities. The method is numerically verified using the marching-on in time algorithm that will be developed in Part II. It will be demonstrated that, for a PEC sphere with velocity near to the light velocity in the vacuum, the scattered fields calculated with the proposed method agree very well with the Lorentz-Mie analytical results obtained using the frame hopping technique.