ASSESSMENT OF THE POINCARE SCHEME FOR NONLINEAR OSCILLATORS AND AN IMPROVEMENT OF ITS RANGE OF VALIDITY

被引：1

作者：

ENGIN, H

ASKAR, A

CAKMAK, AS

机构：

[1] Princeton University, Department of Civil Engineering, Princeton

来源：

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 1979年 / 14卷 / 5-6期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1016/0020-7462(79)90004-0

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

The range of validity of the Poincare method is studied by comparison with the exact solution for the anharmonic and Morse oscillators. The exact solutions for these cases are expressible respectively in terms of elliptic and inverse trigonometric functions. The oscillation frequency is taken as the basis for the comparison. It is seen that the Poincare perturbation gives fairly accurate results up to amplitudes that are 20-30 per cent of the maximum value allowed for periodic solutions depending on the form of the potential energy. A new method is presented as a slight variation over the standard Poincare method. This method differs from the former only by a rearrangement of the differential equation through a collocation approximation for the potential. In spite of its simplicity, the method proves to be a better approximation than the standard Poincare method and gives remarkably accurate results for amplitudes up to 60-70 per cent of the maximum value allowed for periodic solutions. © 1979.

引用

页码：305 / 314

页数：10

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