非线性力矩作用下气动偏心弹丸强迫圆锥运动稳定性条件

Forced Conical Motion Stability Conditions for Pneumatic Eccentric Projectile under the Action of Nonlinear Moment

为了指导无伞末敏弹等气动非对称弹丸的结构设计和气动设计,建立了气动偏心弹丸在三次方非线性静力矩和二次方非线性赤道阻尼力矩作用下的攻角方程,运用平均法求解了方程的近似解析解及其线性变分方程。在此基础上,根据Hurwitz判别准则,得到了气动偏心弹丸做强迫圆锥运动的渐近稳定条件,分析了该条件的物理意义,并应用数值计算算例对该条件进行了验证。结果表明,当自转角速度和气动偏心角满足一定的约束条件时,三次方非线性静力矩和二次方非线性赤道阻尼力矩作用下的弹丸可以实现固定攻角的稳定强迫圆锥运动。

An angle of attack equation of pneumatic eccentric projectile under the action of cubic nonlin- ear static moment and quadratic nonlinear equatorial damping moment is established for the structure de- sign and aerodynamic design of pneumatic asymmetric projectiles, such as non-parachute terminal sensi- tive projectile, and the approximate analytical solution of the equation and linear variational equation are solved by using average method. On this basis, the asymptotic stability conditions of forced conical mo- tion for pneumatic eccentric projectile is obtained according to Hurwitz criterion, and the physical mean- ing of the conditions is analyzed. The numerical calculation example is used to verify the conditions. Re- sult shows that the projectile under the action of cubic nonlinear static moment and quadratic nonlinear e- quatorial damping moment can achieve steady forced conical motion at fixed angle of attack when spin ve- locity and pneumatic eccentric angle satisfy certain constraint conditions.