A different approach from that in Chapter 8 is used to extend the analysis to a threedimensional shock whose upstream flow may be nonuniform. The distinction in the preceding chapter between angles based on
V1 and the x-coordinate will no longer
be necessary. The quantities
F(xi), v1,i, p1, ρ1 (9.1)
are presumed known functions of the xi and are sufficiently differentiable, as needed. For Sections 9.3 through 9.8, these parameters are time independent; a steady flow is assumed. The last two sections, however, consider the unsteady case, and parameters, such as v1,i, now explicitly depend on xi and t. Knowledge of these items are the necessary and sufficient conditions for the analysis in this chapter. The above items parallel the approach discussed in Section 4.1 and should result in a computer-friendly set of algorithms. This approach provides a seamless transition from CFD or experimental data, in a laboratory frame, to the shock-based frame of the theory.