Approximate first integrals of weakly nonlinear, damped-driven oscillators with one degree of freedom

Unal G.

NONLINEAR DYNAMICS, vol.26, no.4, pp.309-329, 2001 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 4
  • Publication Date: 2001
  • Doi Number: 10.1023/a:1013331523696
  • Journal Name: NONLINEAR DYNAMICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.309-329
  • Istanbul Technical University Affiliated: No

Abstract

First-order approximate symmetries of weakly nonlinear, damped-driven oscillators have been determined. First-order approximate first integrals have been obtained by employing an approximate version of Noether's theorem for the conservative case. Furthermore, approximate first integrals of the damped case have been obtained based on the first integrals of the conservative case. Approximate first integrals enabled us to identify three types of generic bifurcations. Analytical results have been verified by numerical experiments.