四元数在弹射座椅性能仿真中的应用

针对弹射座椅性能仿真中欧拉角速率方程在大幅度姿态运动时存在奇异性,以及四元数法由于姿态角的有界性而出现跳跃、难以实现全姿态角的问题,提出了四元数与欧拉角相结合的方法.阐述了四元数的定义、几何意义及四元数表示的运动学方程.通过四元数到欧拉角的转换,给出了仿真中四元数的积分初值计算公式;分析了弹射仿真中姿态角的跳跃和间断问题.以某型号座椅为例进行了仿真计算,通过对比仿真结果和试验数据,确认了仿真的有效性;与采用单一四元数法的仿真结果进行对比表明,该方法充分结合了四元数与欧拉角速率方程的优点,有效解决了欧拉角速率方程的奇异性和弹射仿真中全姿态角的实现. 

Application of quaternion in ejection seat performance simulation

A new method of combined quaternion and Euler angle was proposed to solve the singularity problem of Euler angle velocity equation at large extent attitude movement and all-attitude angles and jumping problems for the limitary of attitude angle using quaternion method in ejection seat performance simulation.Quaternion definition and geometry meaning were described and quaternion movement equation was introduced.Calculation formula of quaternion integral initial values in simulation was put forward through quaternion to Euler angle conversion. The problem of attitude angle jumping and discontinuous in simulation was analyzed.Simulation based on certain seat model was executed.Compared simulation result with experiment data and compared the result with another simulation using single quaternion method,it was shown that this method combined the virtue of quaternion and Euler angle velocity equation could efficiently resolve the singularity of Euler angle velocity equation and could realize all-attitude angle in simulation.