The relationship between the shock velocity and the particle velocity
Abstract
It is shown that the linear relationship between the shock velocity and the particle velocity can be obtained as a consequence of the RankineHugoniot equations, if one assumes in addition that for every material there exists a maximum value for the shock compression. The linear relationship results then as a particular solution of a differential equation. It is also shown that the general solution is not linear, but that its asymptotic behavior must be linear.
 Publication:

Sciences et Techniques de l'Armement (Memorial de l'Artillerie Francaise
 Pub Date:
 1975
 Bibcode:
 1975stam...49..325P
 Keywords:

 Asymptotic Methods;
 Particle Motion;
 Propagation Velocity;
 RankineHugoniot Relation;
 Shock Wave Propagation;
 Differential Equations;
 Discontinuity;
 Independent Variables;
 Linear Systems;
 Fluid Mechanics and Heat Transfer