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 non-zero 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.
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