This paper is concerned with the symbolic computation of the normal forms of general multiple-degreeof-freedom oscillating systems. A perturbation technique based on the method of multiple time scales, without the application of center manifold theory, is generalized to develop efficient algorithms for systematically computing normal forms up to any high order. The equivalence between the pertu...

The three-level atomic system interacting with one mode of the electromagnetic field in a ,'q,-cortfigurafion is investigated. Effective Hamiltonians for two-photon processes without the rotating wave approximation are obtained by application of the perturbation method of multiple time scales. Some inaccuracies in the form of Hamiltonians of this type recently presented are pointed out and corr...

AbstractThe paper involves thorough study of non-linear vibratory oscillators and numerical methodology to analyse and resolute the non-linear dynamical world. The study involves the analysis of non-linear oscillators like the Van der Pol Oscillator and Duffing Oscillator. Application of regular perturbation method in the oscillator is also demonstrated. The equilibrium and stability analysis o...

the current paper focuses on some analytical techniques to solve the non-linear duffing oscillator with large nonlinearity. four different methods have been applied for solution of the equation of motion; the variational iteration method, he’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. the results reveal that approximation obtained by th...

A perturbation technique has been developed in Part I to consider the computation of the normal forms for general multiple-degree-of-freedom autonomous systems. In this paper, the perturbation approach is extended to study general non-autonomous systems and is focused on systems with external forcing. With the aid of multiple time scales, efficient recursive algorithms are developed for systema...

There are typically several perturbation methods for approaching the solution of weakly nonlinear vibrations (where terms “small” compared to linear ones): Method Strained Parameters, Naive Singular Perturbation Method, Multiple Scales, Harmonic Balance and Averaging. The Straightforward Expansion (SEPM) applied does not usually yield correct solutions. In this manuscript, we provide mathematic...

For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono has been shown to be an effective general approach. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the PoincareLindstedt method, the method of averaging, and others. ...