Simulation of Torpedo Air Trajectory Based on Dual-Euler Method

Due to its advantages of obtaining torpedo’s attitude angle and position intuitively, Euler angle representation has been extensively applied to solve the differential equation of torpedo’s six-DOF motion. However, for the torpedo air trajectory, this representation will produce singular points at the pitching angles of ± 90°, leading to the fact that the Euler equation cannot be solved. Therefore, this paper employs the dual-Euler method to avoid such singularity. Based on the dual-Euler method, a mathematical model of torpedo motion is established, and the torpedo air trajectory is numerically simulated. There is no divergence induced by the singularity during the calculation process. Simulations result shows that the torpedo air trajectory model based on the dual-Euler method can reflect the motion characteristics of torpedo air trajectory, and can achieve satisfactory performance at arbitrary angles. This work may provide a theoretical reference for the study of torpedo air trajectory.