Medium to high velocity linear sliding contact is modeled as the response of an elastic half space to an unlubricated punch, moving at constant speed. The stresses in the half space are derived explicitly, using the singular integral equation technique pioneered by Muskhelishvili. The solution is shown to satisfy all necessary mathematical and physical conditions, including an accurate prediction of the Rayleigh surface wave velocity. The normal stresses are evaluated and plotted to demonstrate the interplay between friction and inertial effects at various velocities.

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