478 
where R is the radial coordinate of the shock front, 1 yp and nv are 
unit vectors in the radial direction and in the direction of the normal 
to the shock front, respectively, and VY r is the deformation-rotation 
dyadic. The components of VI are easily found at the shock front from 
the fact that the medium experiences a pure strain of magnitude RB lp -1 
in a direction normal to the shock front as the result of the passage of 
the wave. If the operator d/d is applied to the Hugoniot relation between 
the pressure and particle velocity normal to the shock front and to the re- 
lation describing continuity of the tangential component of particle veloc- 
ity at the shock front, there result 
A 
2. (1gn = a deh (9.3) 
3 = 96 Pa) = bd bog U/d boy fe, - 
The derivation of the approximate energy relation which avoids 
the explicit integration of the equations of hydrodynamics is analogous to 
that of section 8. The adiabatic work W, per unit area of initial generating 
surface done on the fluid exterior to a generating cylinder is given by 
R 60 
21a, d Zw. hs PoE [ja n(rg) J2migdz, dr; + (R,Z) (p+p) uo dt . 
a, tir) (9h) 
where U ad ik denote particle velocity and excess pressure behind the shock 
vee, 
front, t( A) is the time of arrival of the shock front at the point with 
Lagrange cylindrical coordinates Up = R, Z = Z(R ) 5 E(p is the 
specific energy increment of the fluid at pressure bo for the entropy incre- 
88 
