This review features a survey of some recent developments in asymptotic techniques and
new developments, which are valid not only for weakly nonlinear equations, but also for …

This review paper is concerned with the applications of Jacobi elliptic functions to nonlinear
oscillators whose restoring force has a monomial or binomial form that involves cubic and/or …

The so-called Lidov-Kozai oscillation is very well known and applied to various problems in
solar system dynamics. This mechanism makes the orbital inclination and eccentricity of the …

This book presents and extend different known methods to solve different types of strong
nonlinearities encountered by engineering systems. A better knowledge of the classical …

An analytical approximate technique for large amplitude oscillations of a class of
conservative single degree-of-freedom systems with odd non-linearity is proposed. The …

This paper deals with the nonlinear oscillations of a particle which moves on a rotating
parabola. An analytic approximate technique, namely optimal homotopy asymptotic method …

In this paper, the nonlinear dynamic behaviour of an electrical machine exhibiting nonlinear
vibration is investigated using a new analytical technique, namely Optimal Homotopy …

The notion of homotopy is an important part of topology and thus of differential geometry.
The homotopy continuation method or shortly speaking homotopy was known as early as in …

The homotopy perturbation method is used to solve the Duffing-harmonic oscillator. Only
one iteration leads to high accuracy of the approximate solution, which is valid for the whole …

Featured Application This is a novel procedure for solving nonlinear equations of vibrations
with asymptotic solutions. It is an extension to the popular Galerkin method by adding an …