481 
The function F(R - v) is the energy-time integrand, normalized by its peak 
value at the shock front, expressed as a function of R and a reduced time + 
which normalizes its initial slope to -l if it does not vanish. 
At the shock front, 154 us va =n sim 8 , where D 
is the angle between the tangent to the wavefront and the Y -axis, The 
desired energy-equation is obtained by eliminating (+ between the first two 
of Eqs. 9.11 and making use of the Hugoniot relations. As the result, one 
obtains 
(ale feen BG + del (Le eu] 
= -usen [ XP y Hon | 
D(R) RY 
where V,uc, is the Euler rate of strain dyadic, and where each term is eval- 
uated at the shock front. The shock-wave energy at F per unit area of ini- 
tial generating surface is D(K)/a, » Where Gis the Lagrange radial 
coordinate of the generating surface and DR) is given by 
dD ~ _» Rh(p_) 
a - Po MP? , (9.13) 
obtained by differentiation of the definition of the energy variable W i) ’ 
Eq. 99. 
As in the case of the spherical wave, y= | for the peak approx- 
imation to the Lagrange energy-time curve, and the assignment of this value, 
independent of the coordinates, is equivalent to imposing a similarity re- 
straint on the energy-time curve. 
In order to obtain the propagation equations for the one= 
dimensional wave, the origin of the radial coordinate r is taken to be 
oz 
