A Functional-Differential System of Neutral Type Arising in a Two-Body Problem of Classical Electrodynamics

Abstract

This chapter discusses functional-differential system of neutral type arising in a two-body problem of classical electrodynamics. The functional-differential system is referred as neutral system because of its resemblance to the equation y′(t) = f(t,y(t), y(g(t)),y′(g(t)))for t>t0. The term apparently arose because in certain simple cases, the equation is equally considered as having a retarded argument or an advanced argument. The equations of motion for the two-body problem of classical electrodynamics have certain singularities. Thus, it is important to assume restricted domains of definition for the functions f and g. As the solution does not have any more than a piecewise continuous derivative, nothing is gained by imposing more than piecewise continuity conditions on φ′(t) The chapter is restricted to the two-body problem partly for simplicity and partly to emphasize that the existence theorems are studied at present for functional-differential system.