Improvement of dual-Euler method for full scale Eulerian angles solution of aircraft

To overcome the shortcoming of the original dual-Euler method, i.e., it presumes that the range of pitching angle was limited to[-90°, + 90°] and it can't be used for continuous solution of super-maneuvering flight when the pitching angle was beyond this limited range, improvement was made to solve Eulerian angles for full scale continuously by introducing a discriminant function that can obtain the only one corresponding solution for both positive Eulerian system and negative Eulerian system. To validate the new method, a simple model of super-maneuvering was numerically simulated with the improved Dual-Euler method, and R-K algorithm with variant time steps was used for time integration. Results showed that the numerical solution was in perferct agreement with the theoretical solution.