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钟扬威 , 王良明 , 傅健 , 等 . 弹箭非线性角运动稳定性Hopf分岔分析 [J ] . 兵工学报 , 2015 , 36 ( 7 ): 1195 - 1202 . DOI: 10.3969/j.issn.1000-1093.2015.07.007 http://doi.org/10.3969/j.issn.1000-1093.2015.07.007 为了分析弹箭的角运动稳定性，推导了弹箭的非线性角运动方程组，给出弹箭的非线性角运动Hopf分岔分析方法。以某型火箭弹高原试验为例，选取空气密度作为分岔参数，采用霍尔维茨判据判断了系统的稳定性，并确定了分岔点。由中心流形定理对系统进行降维，计算了Hopf分岔的3阶规范形，并作出了系统的分岔图，分析了分岔参数对极限环摆幅的影响。进行了仿真验证，结果表明，采用分岔分析方法能准确判断系统的稳定性及分析系统的极限环运动。

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杨杰 , 常思江 , 魏伟 . 带扰流片旋转稳定弹动态稳定性 [J ] . 兵工学报 , 2021 , 42 ( 8 ): 1613 - 1623 . DOI: 10.3969/j.issn.1000-1093.2021.08.005 http://doi.org/10.3969/j.issn.1000-1093.2021.08.005 为发展一种新型弹道修正弹，以带扰流片旋转稳定弹为研究对象对其进行动态稳定性分析。推导带扰流片旋转稳定弹的动力学模型并简化得到其非齐次角运动方程，求得攻角在阶跃激励下的瞬态响应和稳态响应解析解。根据非线性角运动方程分析旋转弹结构参数、飞行参数和气动参数对系统分岔特性及稳定性的影响，通过数值计算分析带扰流片旋转稳定弹的修正能力。结果表明：求得的攻角解析解具有较高的精度；气动参数对动力学系统平衡点的稳定域影响较大；扰流片的控制效率很高。研究结果为带扰流片旋转稳定弹的结构参数设计提供了参考。

YANG J , CHANG S J , WEI W . Dynamic stability of spin-stabilized projectile with spoiler [J ] . Acta Armamentarii , 2021 , 42 ( 8 ): 1613 - 1623 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2021.08.005 http://doi.org/10.3969/j.issn.1000-1093.2021.08.005 The dynamic stability of spin-stabilized projectile with spoiler is analyzed to develop a new type of trajectory correction projectile. The dynamic model of the spin-stabilized projectile with spoiler is derived and simplified to obtain its non-homogeneous angular motion equation. The analytical solutions of the transient and steady-state responses of angle of attack under step excitation are obtained by using the non-homogeneous angular motion equation. The effects of structural, flight and aerodynamic parameters on the bifurcation characteristics and stability of the system are analyzed based on the nonlinear angular motion equation. The correction ability of the spin-stabilized projectile with spoiler was analyzed by numerical calculation. The results show that the analytical solution of the angle of attack has high accuracy, the aerodynamic parameters have a great influence on the stability region of the equilibrium point of the dynamic system, and the control efficiency of the spoiler is very high.

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KHODADADI L , SAMADI B , KHALOOZADEH H . Estimation of region of attraction for polynomial nonlinear systems: a numerical method [J ] . ISA Transactions , 2014 , 53 ( 1 ): 25 - 32 . DOI: 10.1016/j.isatra.2013.08.005 http://doi.org/10.1016/j.isatra.2013.08.005 This paper introduces a numerical method to estimate the region of attraction for polynomial nonlinear systems using sum of squares programming. This method computes a local Lyapunov function and an invariant set around a locally asymptotically stable equilibrium point. The invariant set is an estimation of the region of attraction for the equilibrium point. In order to enlarge the estimation, a subset of the invariant set defined by a shape factor is enlarged by solving a sum of squares optimization problem. In this paper, a new algorithm is proposed to select the shape factor based on the linearized dynamic model of the system. The shape factor is updated in each iteration using the computed local Lyapunov function from the previous iteration. The efficiency of the proposed method is shown by a few numerical examples. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

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