Hopf Bifurcation Analysis of a Nose Landing Gear System of Aircraft

Abstract

The Hopf bifurcation problem of a nose landing gear system is investigated. Taking the nearly smooth landing gear system with high-order nonlinear terms as the research object, the nose landing gear system is simplified to a plane dynamic system considering nonlinear factors by using the center manifold simplification method. The first Lyapunov coefficient of the landing gear system is derived by using the classical bifurcation theory, and the Hopf bifurcation type of the system is determined according to its sign. The bifurcation diagram is obtained by solving the differential equations of motion numerically. It is revealed that there is a stable limit cycle in the neighborhood of the supercritical Hopf bifurcation point. The influence of velocity and other factors on the shimmy oscillations of the landing gear system is analyzed. The dynamical behavior in the neighborhood of the Hopf bifurcation point is explored theoretically and numerically. The research results can provide a theoretical basis for the optimal design of aircraft landing gear systems.