Use of Bifurcation and Continuation Methods for Aircraft Trim and Stability Analysis - A State-of-the-Art

TLDR

Bifurcation and continuation methods have evolved into a powerful tool over the past two decades for analyzing aircraft trim and stability, addressing high‑angle‑of‑attack behavior, spin, rolling instabilities, and supporting flight‑control design and evaluation. This paper surveys the state‑of‑the‑art application of bifurcation and continuation techniques to aircraft trim and stability analysis, illustrated with several examples. The authors review and demonstrate how these methods are applied to trim and stability problems, providing illustrative case studies. The review demonstrates that both standard and extended bifurcation analyses predict instabilities in high‑α flight and inertia‑coupled roll maneuvers, and yield analytical instability criteria for roll‑coupling and wing‑rock problems. The paper cites 76 references.

Abstract

The bifurcation and continuation methodology has evolved over the last two decades into a powerful tool for the analysis of trim and stability problems in aircraft flight dynamics. Over the years, bifurcation methods have been employed to deal with a variety of problems in aircraft dynamics, such as predicting high angle of attack behavior, especially spin, and studying instabilities in rolling maneuvers. The bifurcation methodology has served as a tool for the design of flight control systems, and is promising to be a useful tool in the aircraft design, simulation, testing, and evaluation process. In the present paper, we describe the state-of-the-art in the use of bifurcation and continuation methods for the analysis of aircraft trim and stability with a few illustrative examples. Both the standard and extended bifurcation analysis procedures are discussed and typical results for instabilities in high-α flight and in inertia-coupled roll maneuvers are shown. This is followed by several problems in nonlinear flight dynamics where bifurcation and continuation methods have been fruitfully applied to yield effective solutions. Finally, the use of bifurcation theory to arrive at analytical instability criteria is demonstrated for the aircraft roll coupling and wing rock problems. 76 references have been cited in the text.