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RESEARCH PAPERS

Symmetric Arc Solutions of ζ̈ = ζn

[+] Author and Article Information
C. P. Atkinson

Division of Applied Mechanics, University of California, Berkeley, Calif.

B. L. Dhoopar

Indian Institute of Technology, Kanpur, India

J. Appl. Mech 35(3), 565-570 (Sep 01, 1968) (6 pages) doi:10.1115/1.3601252 History: Received November 03, 1967; Online September 14, 2011

Abstract

This paper, “Symmetric Arc Solutions of ζ̈ = ζn ,” presents periodic solutions of this differential equation relating the complex variable ζ(t) = u(t) + iv(t) and its second time derivative ζ̈ 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).

Copyright © 1968 by ASME
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