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variables but retain the Euler equation of continuity. Eqs. 8.5 are to be 
solved, subject to initial conditions specified on a curve in the GS LE )- 
plane, and to the Rankine-Hugoniot conditions (Eqs. 2,2) at the shock front, 
aye 
rT al 
SS 
aa 
\ = 
"sles. 
— 
NS 
(8.6) 
(o 
where /\H is the specific enthalpy increment experienced by the fluid in 
traversing the shock front, and U is the velocity of the shock front. The 
Hugoniot conditions constitute supernumerary boundary conditions, compatible 
with the differential equations and specified initial conditions, only if _ 
the shock front follows an implicitly prescribed curve Rit) in the (r,t )- 
plane. Having thus stated the mathematical problem, we shall describe an 
approximate method of avoiding the explicit integration of the partial dif- 
ferential equations. 
We shall denote a derivative in which the shock front is stationary 
by 
renee ole dt 2] 
ER ou pea yee or TAR Ot eee 
Seiny 
dr, U dt ek 
If the operator aldr is applied to the first of the Hugoniot relations 
‘ (8.7) 
i 
(Eqs. 8.6), and if Eqs. &.5 are specialized for the shock front, yy = Ip, we 
obtain the following three relations for the four partial derivatives dp/ot,, 
