Freedom in Small Parameter Expansion for Nonlinear Perturbations

The freedom of choice of the zero-order term in the perturbative analysis of harmonic oscillators that are perturbed by a nonlinear perturbation is investigated in detail within the framework of the method of normal forms in the case of the unforced Duffing oscillator. It is demonstrated that the ch...

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Veröffentlicht in:	Proceedings of the Royal Society. A, Mathematical and physical sciences Mathematical and physical sciences, 1993-10, Vol.443 (1917), p.83-94
Hauptverfasser:	Kahn, Peter B., Murray, Diana, Zarmi, Yair
Format:	Artikel
Sprache:	eng
Schlagworte:	Approximation Coefficients Exact sciences and technology Freedom of choice Function theory, analysis Harmonic oscillators Mathematical functions Mathematical independent variables Mathematical methods in physics Mathematical transformations Ordinary differential equations Oscillators Physics Resonance Series convergence
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Beschreibung
Zusammenfassung:	The freedom of choice of the zero-order term in the perturbative analysis of harmonic oscillators that are perturbed by a nonlinear perturbation is investigated in detail within the framework of the method of normal forms in the case of the unforced Duffing oscillator. It is demonstrated that the choice leading to minimal normal forms (MNF) is by far the best, indicating that MNF may be a way to significantly improve the convergence properties of the perturbation series relative to the traditional expansions.
ISSN:	1364-5021 0962-8444 1471-2946 2053-9177
DOI:	10.1098/rspa.1993.0132