High-speed penetration of a solid sphere into the soil (Q1280379)

The author examines the penetration of a rigid sphere into the soil. The soil is modelled by an ideal non-viscous plastic compressible liquid occupying the lower half-space, and the penetration is considered normal to the plane horizontal surface of the soil. For the solution the author uses the Lighthill approximations which have been obtained earlier for the problem of stationary hypersonic gas flow around a sphere.