Pendulum-Like Systems Of A Certain Class Of Nonlinear Differential Equations - A Review∗

Abstract

From the ideal pendulum equation of second order non-linear differential equation

x¨ + b sin x = 0

to the damped and forced equations, we look at the generalized mathematical pendulum and systems associated with it. The works of M.L.Cartwright & J.E. Littlewood, J.O.C. Ezeilo and H.O. Tejumola are indicated. The generalization to systems with multiple-equilibria, canonical forms, reduction methods and generalizations to higher-order differential equations are highlighted. Pendulum-like systems of third order are given as examples, for dichotomy and gradient-like solutions. Challenges to Nigerian Mathematical Society are highly emphasised in conclusion.