Mathematical Analysis of Corotating Nose-Gear Shimmy Phenomenon

A derivation of the equation of motion of a nose gear having four degrees of freedom is presented. These equations are obtained by using a special form of the powerful Lagrangian formalism. This approach demands relatively little physical intuition and produces rigorous results. This derivation yields the differential equations of motion in their unlinearized form to make possible an investigation of shimmy amplitude for the proper design of damping devices. Such information about shimmy amplitude is not forthcoming from the linearized form of the differential equations, which are amplitude-independent. Only the linearized differential equations are at present found in the literature. A detailed comparison of the linearized form of the equations of motion here derived, with those developed by Moreland, is also presented with discussion of several points of interest revealed by the formalism here employed.