旋转稳定二维弹道修正弹在固定舵作用下的角运动特性研究

为研究旋转稳定二维弹道修正弹在固定舵作用下的攻角及速度运动特性,建立了复数形式的角运动方程。推导了固定舵匀速转动时攻角的强迫运动解及固定舵产生阶跃激励时攻角的瞬态、稳态响应解析解;推导了有控时平均速度偏角的解析解,导出了平均偏角的幅值和相位角与固定舵参数的关系;提出了旋转稳定二维弹道修正弹在固定舵作用下的飞行稳定性条件。结果表明:二维弹道修正弹无控时应避免共振,有控时应限制攻角最大增量及平衡攻角幅值;有控时平均偏角的相位角较固定舵滚转角提前一个前置角。研究结果对旋转稳定二维弹道修正弹的飞行稳定性设计及制导方法研究提供了参考。

Study on Angular Motion Characteristics of Spin-stabilized 2D Trajectory Correction Projectile under the Effect of Fixed Canards

An angular motion equation in complex form is established to study the angle of attack and velocity characteristics of spin-stabilized 2D trajectory correction projectile under the effect of fixed canards.The solution of forced motion when the canards spin at a constant rate and the analytical solutions of transient and steady state responses when the canards generate step excitation are both derived.The relationships between the amplitude and phase angle of average deflection angle and the parameters of the fixed canards are presented by deriving the analytical solutions of average velocity deflection angle.The flight stability conditions of spin stabilized 2D trajectory correction projectile under the effect of fixed canards are proposed.The result shows that the projectile should avoid resonance without control,and should limit the maximum increment of angle of attack and the equilibrium angle of attack with control.In addition,the phase angle of average deflection angle has a lead angle ahead of the roll angle of fixed canards.The results provide some references for the studies of flight stability and guidance method of spin-stabilized 2D trajectory correction projectile.