Hodograph transformation

Summary

The hodograph transformation exchanges the roles of position and velocity in a steady planar flow. Instead of the velocity $(u, v)$ as a function of the position $(x, y)$, one studies $(x, y)$ as a function of $(u, v)$ in the hodograph plane. For steady irrotational compressible flow this turns the nonlinear equations of motion into linear equations, such as Chaplygin's equation. It was a main source of exact solutions in transonic flow theory. See the definition.