Basic methods for stability analysis of nonlinear oscillations and waves
Abstract
Attention is given to the way in which linear stability analysis, Liapunov analysis, and the Nyquist diagram lend themselves to the study of plasma stability. It is pointed out, however, that their application is not limited to the field of plasma physics. A comprehensive (nonspecialized) discussion of these methods for the stability analysis of nonlinear oscillations and waves is presented. The multidimensional conservative system is discussed, and an example is adduced showing how the energy principle permits a quick answer to the question of stability. Attention is also given to Gardner's theorem.
- Publication:
-
Arabian Journal of Science Engineering
- Pub Date:
- April 1983
- Bibcode:
- 1983AJSE....8...87H
- Keywords:
-
- Liapunov Functions;
- Linear Equations;
- Nonlinear Systems;
- Nyquist Diagram;
- Stable Oscillations;
- Systems Stability;
- Wave Equations;
- Energy Conservation;
- Equilibrium Equations;
- Magnetohydrodynamic Stability;
- Saturation;
- Physics (General)