Define the relative speed of propagation of the singular surface S by U = V v n, where V is the speed of propagation of the surface in the current configuration, and define U = V v n and U = V v n. Use the basic jump conditions to derive the following results: (a) U U[[]] = [[t n]] (this is the Rankine-Hugoniot relation) (b) If the singular surface is also a material surface, [[t]] = 0 , [[v n]] = 0 (c) If, in addition to (b), the stress is spherical (T = I) [[q n]] = 0 (d) In an isochoric motion no shock wave can exist