Weighted linearization technique for period approximation in large amplitude non-linear oscillations

Abstract

Period approximations for conservative, one-dimensional, non-linear oscillating systems are considered. The approximation technique used is linearization of the non-linear restoring function governing the system. While in previous papers the best period approximations in the small amplitude limit have been discussed, the best large amplitude results are investigated herein, with use of linearization based on weight functions of the power type. The non-linear functions examined here are odd polynomials, sine, hyperbolic sine, tangent, and hyperbolic tangent. © 1985.