四元数法在双翼无伞末敏弹仿真中的应用  

Application of Quaternion Algorithm in Simulation of Terminal Sensitive Projectile

作　　者：胡志鹏[1] 刘荣忠[1] 郭锐[1] 邱荷[1] 

机构地区：[1]南京理工大学智能弹药技术国防重点学科实验室,江苏南京210094

出　　处：《计算机仿真》2013年第1期14-17,共4页Computer Simulation

基　　金：国家自然科学基金青年科学基金项目(11102088);教育部博士点基金新教师类(20093219120006)

摘　　要：传统无伞末敏弹六自由度仿真多基于欧拉角方法求解运动微分方程,上述方法可以直观地得到无伞末敏弹的位置和姿态角,但在倾角±90°的情况下会产生奇异点,使计算误差较大,得不到正确结果。为克服上述不足,采用四元数表示欧拉角和欧拉方程,建立双翼无伞末敏弹的稳态扫描运动数学模型,并对稳态扫描运动进行数值计算。仿真结果表明,基于四元数法的弹道模型能够正确地反映双翼型无伞末敏弹的稳态扫描运动规律,在计算过程中不会因出现奇异点而发散,并可以进行任意角度的仿真。仿真结果表明,采用的动力学模型可以用于无伞末敏弹大幅度姿态运动的总体设计等研究中。Due to its advantages of describing non parachute terminal sensitive projectile （TSP） ＇ s attitude angle and position in a simple and direct way, Euler angle representation has been extensively applied to solve the differentiating equation of TSP＇ s six-DOF motion. However, this representation is undefined for a pitch angle of ±90 degree and will lead to the simulation cannot be done at those angles. An alternative to avoid such singularities is to apply the quaternion representation. Based on the quaternion representation, the stable scanning model was established, and the motion of stable scanning was numerically simulated. There is no divergence during the calculation process. The simulations show that the quaternion trajectory model can reflect the characteristics of stable scanning motion of TSP correctly and its improvement over Euler angle representation by achieving the satisfactory performances with arbitrary angles. The dynamic model is useful for the general design of large attitude maneuver of TSP.

关 键 词：四元数法 末敏弹 稳态扫描 弹道方程 

分 类 号：TJ011[兵器科学与技术—兵器发射理论与技术]