用于大机动飞行仿真的四元数改进算法

Modified Quaternion Method in High Maneuver Flight Simulation

传统的四元数和欧拉角之间的转换只在[-90o,90o]之间取值,且仅是对体轴系下的姿态角进行处理,并没有考虑与航迹轴相关的航迹角的转换问题,这样在大机动飞行仿真中不仅会使飞机方程的解出现奇异,且不能正确表示飞机的姿态。提出了一种新的改进算法,使用该算法,不仅能够实现全角度的四元数与欧拉角之间的转换,也对航迹角的解算进行了相应的处理,使仿真结果与姿态角和航迹角的定义及定义域吻合,能够正确描述飞机的飞行状态。经过对多种大机动飞行动作的仿真,验证了本方法是正确、实用的。

In traditional method of transformation between quaternion and Euler angle, the Euler angle was ranged only over [-90°, 90°] and transformation of flight path angle was seldom considered. It could result in singularity solution to the flight dynamic equation and incorrect expression of flight attitude. A new algorithm which can cope with a large-scale transformation between quaternion and Euler angle ranged into [-180°, 180°] was proposed. The flight path angle transforming method was also described here, so as to get the real solution of flight dynamic equation. Digital simulation results of a lot of maneuvers show that the method is perfectly feasible and applicable in engineering practice.