Abstract
Exact symmetries of the unperturbed (linear) part of the dynamical systems are determined. Resonance conditions which lead to the symmetry-breaking of the symmetries of the unperturbed part are obtained. The second-order approximate symmetries of the one degree of freedom, damped-driven oscillators are found. By employing an approximate version of Noether's theorem, second-order approximate first integrals are obtained for undamped oscillators. The results are discussed on the contour plots of the first integrals.
| Original language | English |
|---|---|
| Pages (from-to) | 258-267 |
| Number of pages | 10 |
| Journal | Bulletin of the Technical University of Istanbul |
| Volume | 51 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1999 |
Keywords
- Approximate first integrals
- Approximate symmetries
- Oscillators
- Resonances
- Symmetry-breaking