Vehicles moving on rough surfaces are subject to inputs which are often conveniently regarded as random processes. In general, the excitation process is “perceived” by the vehicle as a nonstationary random process either due to inhomogeneity in the ground profile or variations in the vehicle’s velocity, or both, Hitherto this second case has not been tractable analytically due to the time variable delay between inputs. In this paper this difficulty is overcome and expressions are derived for the propagation of the mean vector and zero-lag autocovariance matrix. An example of a vehicle modelled by a bicycle configuration is discussed.

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