Bifurcation analysis of nose landing gear shimmy with lateral and longitudinal bending

We develop and study a model of an aircraft nose landing gear with torsional, lateral and longitudinal degrees of freedom. The corresponding three modes are coupled in a nonlinear fashion via the geometry of the landing gear in the presence of a nonzero rake angle, as well as via the nonlinear tyre forces. Their interplay may lead to different types of shimmy oscillations as a function of the forward velocity and the vertical force on the landing gear. Methods from nonlinear dynamics, especially numerical continuation of equilibria and periodic solutions, are used to asses how the three modes contribute to different types of shimmy dynamics. We conclude that the longitudinal mode does not actively participate in the nose landing gear dynamics over the entire range of forward velocity and vertical force.