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The work reported in this paper concetrates on the possibility of suppressing landing gear shimmy oscillations more effectively using a linear passive suppression device incorporating inerter. The inerter is a one-port mechanical device with the property that the applied force is proportional to the relative acceleration between its terminals. A linear model of a Fokker 100 aircraft main landing gear equipped with a shimmy suppression device is presented. Time-domain optimizations of the shimmy suppression device are carried out using cost functions of the maximum amplitude and the settling time of torsional-yaw motion. Applying two types of excitations which trigger the shimmy oscillations, performance advantages of inerter-based configurations for suppressing amin landing gear shimmy, together with corresponding parameter values, are identified.