22. O.Yu.Zharii, An exact solution of a time-dependent frictional contact problem for two elastic spheres, Int. J. Eng. Sci. v. 34, p. 537-548 (1996).
The paper is devoted to development of an analytical technique for treating contact problems with friction for time-dependent loadings. A particular problem of an intermittent contact between two similar spheres, constrained against the rigid-body rotation, is considered. First, normal tractions are determined from classic Hertz theory. After that, an initial guess for tangential tractions distributions proved to be consistent with Coulomb's law of dry friction. Analytical formulae for the tangential force resultant and for characteristics of motion in the contact zone as functions of the angle of incidence are obtained and analyzed.
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