  We consider the problem of uniform steady supersonic Euler flows passing a
straight conical body with attack angles, and study Radon measure solutions
describing the infinite-thin shock layers, particularly for the Chaplygin gas
and limiting hypersonic flows. As a byproduct, we obtain the generalized
Newton-Busemann pressure laws. To construct the Radon measure solutions
containing weighted Dirac measures supported on the edge of the cone on the
2-sphere, we derive some highly singular and non-linear ordinary differential
equations (ODE). A numerical algorithm based on the combination of Fourier
spectral method and Newton's method is developed to solve the physically
desired nonnegative and periodic solutions of the ODE. The numerical
simulations for different attack angles exhibit proper theoretical properties
and excellent accuracy, thus would be useful for engineering of hypersonic
aerodynamics.
