Advances in International Applied Mathematics
Advances in International Applied Mathematics. 2024; 6: (2) ; 10.12208/j.aam.20241008 .
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北方民族大学数学与信息科学学院 宁夏银川
*通讯作者： 马小燕,单位：北方民族大学数学与信息科学学院 宁夏银川；
滚转运动在飞行器的横向稳定性中起着关键作用。为了研究随机激励下三角翼飞行器滚转运动的动力学行为，本文在滚转运动模型中引入色噪声激励。首先借助幅值包络随机平均法计算得出FPK方程和振幅响应的平稳概率密度函数。其次，根据奇异性理论，得出系统产生随机P分岔的约束条件。最后，根据该约束条件数值验证了噪声强度与关联时间并不能诱导系统发生随机分岔，而阻尼参数会使系统发生随机P分岔。
Roll motion plays a key role in the lateral stability of the aircraft. In order to study the dynamic behavior of delta-wing aircraft rolling motion under random excitation, color noise excitation is introduced into the rolling motion model. Firstly, the stationary probability density function of FPK equation and amplitude response is calculated by means of amplitude envelope random average method. Secondly, according to the singularity theory, the constraint conditions for the system to generate random P-bifurcation are obtained. Finally, according to the constraint condition, it is numerically verified that the noise intensity and correlation time can not induce random bifurcation of the system, but the damping parameter can cause random P-bifurcation of the system.
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