The paper presents a nonlinear model describing vibration of the landing gear relative to the fuselage. The model is intended to analyze the dynamic stability of nonswiveling main-gear wheels. The model is used to show that the lateral component of the fuselage speed has a significant effect on the critical shimmy speed Keywords: vibration, dynamic stability, landing gear, fuselage, critical shimmy speed, lateral component of fuselage speedIntroduction. The fuselage and landing gear of an aircraft are known to form a self-excited vibratory system [1]. The self-excited vibration of the landing gear (LG) about the fuselage manifested as intensive wobbling from side to side is called shimmy. Both swiveling (sreerable) and nonswiveling wheels are subject to shimmy [2]. Most shimmy studies regard the uniform and rectilinear motion of an aircraft or a mobile robot with the ground-speed vector in the wheel plane as undisturbed motion. In this case, wheels move without slip [1,3,5,[12][13][14]. This kind of motion is typical for takeoff and landing runs under no crosswind.Despite the large-scale studies of shimmy, maintenance experience indicates the need for further investigation into the causes of LG vibration. This experience includes:-intensive vibration resulting in abrupt (in a run) failure of the LG [9, 17]; -fatigue damage and failure of LG components and members elastically coupled with the fuselage, which may lead to off-design behavior of the LG;-frequent failures of tires; -specific vibration felt in the cockpit after abrupt turn of the nosegear to prevent running off the runway [4].Since the classical work [3], the self-excited vibrations of the LG have been attributed to the interaction of two motions of the LG relative to the fuselage: yaw and roll [5]. Such vibrations cannot arise in a mechanical system with one degree of freedom. Modern analytic tire models were used in [6,7] to describe one-degree-of-freedom friction self-vibrations caused by nonlinear and nonmonotonic interaction of the LG tires with the runway. These vibrations occur in the presence of a considerable lateral component of the fuselage speed.The present paper offers a model to describe vibration of the LG about the fuselage moving in a prescribed manner. The model accounts for two degrees of freedom: yaw and roll. The main differences of this model from the available ones are the following: (a) allowance for the constant lateral component of the fuselage speed, which changes the conditions of energy gain in the mechanical system; and (b) use of an analytic model describing the interaction of tires with the runway [10, 11]. Our mathematical model describes both vibration due to the interaction of the modes and vibration due to the nonmonotonic interaction between the tires and the runway.1. Equations of Motion. The axes of OX X X 1 2 3 form an absolute coordinate frame (Fig. 1). The axes OX 1 and OX 3 lie in the runway plane, and the axis OX 2 is aligned with the local vertical while in motion or with the axis AD of the shock strut

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