Abstract
This paper, "Symmetric Arc Solutions of ζ¨ = ζn," presents periodic solutions of this differential equation relating the complex variable ζ(t) = u(t) + iv(t) and its second time derivative ζ¨ The solutions are called symmetric arc solutions since they form such arcs on the ζ = u + iv-plane. The solutions, ζ(t), are “complex modes” of coupled nonlinear differential equations in the complex variables z1 and z2. Symmetric arc solutions are presented for a range of n from n = 3 to n = 101. Approximate solutions are presented and compared with solutions generated by digital computer. Solutions are presented on the ζ-plane and in the time domain as u(t) and v(t).
