477 
The shock wave generated by a stationary detonation wave traveling 
in the axial direction of an infinite cylinder of an explosive is stationary 
in a coordinate system with origin in the detonation wave, Therefore, the 
Eulerian form of the equations of motion, Eqs, 3.1, is the preferred formu- 
lation for the development of the theory. They may be written in the form 
Du. 
aa hh =~ Vey > Dt ae ee (9.1) 
where Ww is the vector particle velocity, b the pressure in excess of the 
pressure p ; of the undisturbed fluid, eB the density, and ¢ the Euler sound 
velocity. They are to be solved subject to initial conditions specified on 
a curve in the (r ,t)-space Cy is the Euler position vector), and to the 
Rankine-Hugoniot conditions, Eqs. 2.2, which constitute supernumerary bound- 
ary conditions at the shock front that are compatible with the equations of 
hydrodynamics and the prescribed initial conditions only if the shock front 
is an implicitly prescribed curve Ret jin the F , b-space. These relations 
are supplemented by the entropy transport equation, which we shall not use 
explicitly, and by an equation of state of the fluid that permits,in combina- 
tion with the Hugoniot relations, evaluation of all of the properties of 
the shock front as functions of the peak pressure Par e The particle veloc- 
ity WU of the Hugoniot relations, Eqs. 2.2, is here taken to be the component 
of particle velocity normal to the shock front, and the shock velocity U 
is the velocity of the shock front in the direction of its normal, 
For the system with axial symmetry, we denote an operator which 
follows the shock front by 
be AT. an 
aR a (We MS Eo | ee pe ee 
