Simulation of Torpedo Air Trajectory Based on Dual-Euler Method
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摘要: 传统鱼雷弹道六自由度仿真多基于欧拉角方法求解运动微分方程, 可以直观地得到鱼雷的位置和姿态角。但随着鱼雷空投弹道的出现, 在倾角±90°的情况下会产生奇异点, 致使欧拉方程无法求解, 得不到正确结果。为克服上述不足, 文中采用双欧拉法建立鱼雷运动数学模型, 并对鱼雷空中弹道进行数值计算。仿真结果表明, 基于双欧拉法的弹道模型能够正确地反映鱼雷空中弹道运动规律, 在计算过程中不会因出现奇异点而发散。Abstract: 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.
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Key words:
- torpedo /
- air trajectory /
- dual-Euler method
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[1] 曲延明, 周明, 林宗祥. 基于Simulink的飞航式火箭助飞鱼雷空中弹道仿真[J]. 舰船科学技术, 2011, 33(12): 107-111.Qu Yan-ming, Zhou Ming, Lin Zong-xiang. Research on Air Trajectory Simulation of the Cruising Rocket Assisted Torpedo Based on Simulink[J]. Ship Science and Technology, 2011, 33(12): 107-111. [2] 李跃军, 阎超. 飞行器姿态角解算的全角度双欧拉法[J]. 北京航空航天大学学报, 2007, 33(5): 505-508.Li Yue-jun, Yan Chao. Improvement of Dual-Euler Method for Full Scale Eulerian Angles Solution of Aircraft[J]. Journal of Beijing University of Aeronautics and Astronautics, 2007, 33(5): 505-508. [3] 周明, 徐德民. 火箭助飞鱼雷弹道的仿真实现与应用研究[J]. 弹箭与制导学报, 2007, 27(2): 235-238.Zhou Ming, Xu De-min. Infection of Impact Dispersion to the Rocket Assisted Torpedo Detection Probability[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2007, 27(2): 235-238. [4] 王亚东, 袁绪龙, 张宇文. 双欧控制法在运载器水弹道中的应用[J]. 鱼雷技术, 2013, 11(6): 401-405.Wang Ya-dong, Yuan Xu-long, Zhang Yu-wen. Application of Dual-Euler Control Method to Water-Trajectory Design of Missile Carrier[J]. Torpedo Technology, 2013, 11(6): 401-405. [5] 杜阳华, 吴宇. 火箭助飞鱼雷发控及弹道仿真[J]. 指挥控制与仿真, 2014, 36(3): 89-94.Du Yang-hua, Wu Yu. Rocket-assisted Torpedo Fire Control and Ballistic Trajectory Simulation[J]. Command Control & Simulation, 2014, 36(3): 89-94. [6] 王晓娟, 唐世轩, 刘正平. 火箭助飞鱼雷系统建模与空中弹道仿真研究[J]. 弹箭与制导学报, 2003, 23(2): 51-55.Wang Xiao-juan, Tang Shi-xuan, Liu Zheng-ping. The Rocket-Assisted Torpedo System to Set Up the Mold and Air the Trajectory to Imitate the True Research[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2003, 23(2): 51-55. [7] Jia Y, Song B W, Liang Q W, et al. Simulation of Trail Guidance Trajectory of a Model Torpedo Based on MATLAB/ Simulink[J]. Systems Engineering-Theory & Practice, 2006, 26(3): 141-140. [8] 周伟, 张晓今, 寇保华, 等. 双欧拉法在克服伞-弹系统欧拉方程奇异性中的应用[J]. 航天返回与遥感, 2003, 24(3): 4-8.Zhou Wei, Zhang Xiao-jin, Kou Bao-hua, et al. The Application of the Dual-euler Method for Overcoming the Singularity of Euler Equation in Parachute-Missile Sys-tem[J]. Spacecrafts Recovery & Remote Sensing, 2003, 24(3): 4-8. [9] 岳军红, 贺怀清. 克服欧拉方程奇异性的方法[C]//第六届全国交通运输领域青年学术会议论文集. 大连: 第六届全国交通运输领域青年学术会议, 2005.
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