The effects of random external excitation on nonlinear systems with marginally stable/unstable modes is studied within the context of stochastic bifurcation theory. Using the method of stochastic averaging, a Markdv approximation is derived and a perturbation technique is developed to solve the resulting Fokker-Planck equation. It is found that, due to mode interaction through system nonlinearities, deterministic bifurcation characteristics are not preserved in the presence of external random excitation. In general, one critical mode can experience a stabilizing effect at the expense of the other. The theory is then applied to a flight dynamics problem at large angles of attack and sideslip.
ASJC Scopus subject areas
- Control and Systems Engineering
- Aerospace Engineering
- Space and Planetary Science
- Electrical and Electronic Engineering
- Applied Mathematics