双翼型无伞末敏弹稳态扫描运动数学模型

Stable Scanning Model for Non-Parachute Terminal Sensitive Projectile With Two Fins

双翼型无伞末敏弹的运动过程存在强非线性、大攻角、有奇异点等现象,用欧拉角方程描述双翼型无伞末敏弹的角运动学方程时可能会出现奇异点而导致退化,针对此问题,采用四元数表示双翼型无伞末敏弹的欧拉角和欧拉方程,建立了其稳态扫描运动的数学模型,并对稳态扫描运动进行了数值计算.结果表明,基于四元数法的弹道数学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,形成所需要的扫描运动轨迹,在计算过程中不会出现奇点而发散,该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 the phenomenon of strong nonlinearity, large angle of attack and singular points during the flight process of non-parachute terminal sensitive projectile with two fins （NPTSPTF）, the Euler angle equations can not be used to describe its motion with the probable appearance of singular point degenerating. Therefore, quaternion was adopted to represent Euler angles and Euler equations of NPTSPTF, and the stable scanning model was established, and the motion of stable scanning was numerically simulated. Results indicate that the trajectory model based on quaternion can reflect the characteristics of stable scanning motion of NPTSPTF correctly and provide the required scanning trajectory. There is no divergence during the calculation process, and the dynamic model is useful for the general design of large attitude maneuver of NPTSPTF.