## Rankine-Hugoniot Relation

Passing through a shock front moving with a speed , the physical variables , , and change abruptly. Since the basic equations of hydrodynamics is unchanged after chosing a system moving , the continuity equation

 (A.26)

gives an equation for a steady state as
 (A.27)

Considering a region containing the shock front at which extends from to and integrating the above equation, we get
 (A.28)

Thus, we obtain the jump condition conserning the mass coservation as
 (A.29)

where the quatities with suffix 1 are for preshock and those with suffix 2 are for postshock.

Equation of motion for steady state

 (A.30)

gives
 (A.31)

where we used equation(A.29).

Subsections
Kohji Tomisaka 2009-12-10