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During the launch of a car, severe torsional vibration sometimes may occur in its driveline due to somewhat the slipping of the clutch, its intuitive sense for an occupant is the longitudinal vibration of the vehicle, referred to as the launch shudder whose characteristic frequency is from 5 to 25 Hz generally. As the main vibration sources of the driveline and its crucial nonlinear components, the variable stiffness and backlash of the gear meshing are considered, their impacts on the launch shudder are analyzed in this paper. Conformal mapping, finite element method and regression method etc. are the main approaches to calculate the variable meshing stiffness of a gear pair. If this stiffness is get, it can usually be substituted for its approximate analytical expression, just with finite harmonic terms, in Fourier Series form into Ordinary Differential Equations(ODEs) to calculate the vehicle responses with its nonlinearity considered.