482 
the axis of the generating cylinder. Eqs. 9.1, specialized to the shock 
front f= R » together with Eqs. 9.3 and 9.12, provide four nonhomogeneous, 
linear relations between the four nonvanishing time and distance derivatives 
of pressure and particle velocity, evaluated at the shock front, with coef- 
ficients that can be expressed as functions of distance and peak pressure 
through Eqs. 2.2 and the equation of state. The equations can be solved 
for the derivatives and an ordinary differential equation, dp,,/ dA = F (Pan oR), 
formulated with the aid of Eq. 9.12. An additional ordinary differential 
equation for the shock-wave energy is provided by Eq. 9.13. The results are 
3 3 
Ap. ae Pan W (p> )+ YF Bom va (Pm) ; (9.14) 
aR aR m 
Saat 4/Pe Vit 80 “fh Ufo) © Z y) 
Me, ) = 2(1+9) - G 
ett GC 
BU* 2lirgd- & 
Gib.) = 17 Ge UL, Son) a 
Eqs. 9.13 and 9.14 may be integrated numerically, employing tables of the 
rob) = 
functions hp) » 7 (p) ’ Np, ) » which can be constructed by numeri- 
cal methods from the exact Hugoniot curves for the fluid. Eqs. 9.13 and 
9.14 are identical with the relations obtained with the simpler considera- 
tions of the last. section.22/ 
92 
