Approximate Analytical Solutions of A Nonlinear Oscillator Equation Modeling A Constrained Mechanical System - Yamgoué, Serge Bruno; Nana, Bonaventure; Pelap, François Beceau (Journal of Applied Nonlinear Dynamics, 2026)
In this paper, we consider a class of nonlinear oscillators whose equations of motion are in the form of that of a cubic Duffing oscillator extended by a term which is a quadratic monomial in the velocity and whose coefficient is a rational function of the position. We apply a combination of harmonic balance and Newton method to seek analytical approximations to the periodic solutions to the equation. The analysis can be applied directly to the equation in its "natural" rational form or after reducing it to the same denominator and considering only the numerator. The advantages and drawback of these two usages of the method are also discussed.