杨树兴 . 陆军多管火箭武器的发展与思考 [J ] . 兵工学报 , 2016 , 37 ( 7 ): 1299 - 1305 . DOI: 10.3969/j.issn.1000-1093.2016.07.019 http://doi.org/10.3969/j.issn.1000-1093.2016.07.019 论述了陆军多管火箭武器的发展进程，重点介绍其在第二次世界大战以来所走过的增大射程、提高射击密集度和实现制导化3个主要发展阶段。归纳总结了陆军多管火箭武器在发展过程中形成的多联装发射平台、弹体采用旋转体制、大长径比、短时大推力发动机和曲射弹道、静稳定设计等特点，分析上述特点对其制导化发展中带来的优势和挑战，提出陆军多管火管武器未来发展中应重点关注和解决的若干问题：旋转弹捷联惯性导航、动态稳定性理论、弹道规划与控制方法、大推力比长工作时间的先进动力、单线制发射控制技术等。

YANG S X . Progress and key points for guidance of multiple launch rocket systems [J ] . Acta Armamentarii , 2016 , 37 ( 7 ): 1299 - 1305 . (in Chinese)

陈成 , 赵良玉 , 谢浩怡 , 等 . 单通道控制旋转弹角运动的复分析方法 [J ] . 兵工学报 , 2021 , 42 ( 2 ): 308 - 319 .

CHEN C , ZHAO L Y , XIE H Y , et al . Complex analysis for angular motion of a spinning projectile with one pair of canards [J ] . Acta Armamentarii , 2021 , 42 ( 2 ): 308 - 319 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2021.02.009 http://doi.org/10.3969/j.issn.1000-1093.2021.02.009 The stability of coning motion of spinning projectile with one pair of canards cannot be directly analyzed by the analytic method due to the aerodynamic asymmetry. The angular motion model and complex analysis method for the spinning projectile are studied. A complex angle-of-attack motion equation is established, and a scaling factor is introduced to the asymmetric aerodynamic term in the equation. On this basis, the analytical expressions of complex angle-of-attack motion equation under different actuator deflection angles are obtained. The convergence process, steady state and resonance of the model are analyzed. The validity of complex angle-of-attack motion equation is confirmed through numerical simulation, and the cause of resonance instability under sinusoidal actuator deflection is revealed.

丁天宝 , 何朝 , 王良明 , 等 . 高速旋转炮弹宽海拔弹道解算方法 [J ] . 兵工学报 , 2021 , 42 ( 1 ): 209 - 213 .

DING T B , HE Z , WANG L M , et al . Calculation method of firing trajectory of high spinning projectile adapted to wide altitude [J ] . Acta Armamentarii , 2021 , 42 ( 1 ): 209 - 213 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2021.01.024 http://doi.org/10.3969/j.issn.1000-1093.2021.01.024 A new method which gives priority to the idea of theoretical calculation and simulation with data of a few tests is proposed to improve the traditional method of firing table development which depends on live firing test radically. A nonlinear motion equation of projectile coupled attitude is established, which is used to calculate the influence of initial disturbance on mean trajectory. The model of the variation of projectile resistance coefficient with the altitude is improved on the basis of the relational model of the ballistic coincidence coefficient and the firing angle of gun. Based on the feature information extracted from a few of high-precision ballistic test data, the theoretical calculation firing table is modified to achieve higher precision. In order to reduce the principle error of the intersection for two firing tables used on plateau and plain individually, a method of smoothing the connection of two firing tables is created. The correctness of the proposed method is proved by the results of the live fire tests, and the precision of the firing table is high enough, which is fully suitable for the applications at the altitude from 0 m to 4 500 m.

杨树兴 , 赵良玉 , 闫晓勇 . 旋转弹动态稳定性理论 [M ] . 北京 : 国防工业出版社 , 2014 .

YANG S X , ZHAO L Y , YAN X Y . Dynamic stability of spinning missiles [M ] . Beijing : National Defense Industry Press , 2014 . (in Chinese)

YAN X Y , YANG S X , XIONG F F . Stability limits of spinning missiles with attitude autopilot [J ] . Journal of Guidance, Control, and Dynamics , 2011 , 34 ( 1 ): 278 - 283 . DOI: 10.2514/1.51627 http://doi.org/10.2514/1.51627 https://arc.aiaa.org/doi/10.2514/1.51627 https://arc.aiaa.org/doi/10.2514/1.51627

MURPHY C H . Free flight motion of symmetric missiles: BRL-1216 [R ] . Aberdeen Proving Ground, MD,US : U. S. Army Ballistic Research Laboratory , 1963 .

陈亮 , 刘荣忠 , 郭锐 , 等 . 旋转尾翼弹箭极限圆锥运动稳定判据 [J ] . 兵工学报 , 2019 , 40 ( 7 ): 1329 - 1339 . DOI: 10.3969/j.issn.1000-1093.2019.07.001 http://doi.org/10.3969/j.issn.1000-1093.2019.07.001 为获得旋转尾翼弹箭极限圆锥运动稳定判据，针对现有理论方法的不足，提出了改进理论模型。该模型通过对弹箭在准圆运动状态下的振幅平面方程进行泰勒展开，从而充分考虑幅值变化对振幅平面方程中根号项取值的影响；在此基础上，根据不同参数取值情况，对其非零奇点的存在性和稳定性进行分析，导出了弹箭在非线性静力矩和非线性马格努斯力矩作用下形成稳定极限圆锥运动的解析判据，并给出两条仅与攻角方程初始参数相关的综合判据条件J₁>0和J₂>0；以某型旋转尾翼弹箭气动及结构特征参数为例，对所得理论判据进行了验证。研究结果表明，给出的稳定极限圆锥运动形成判据，与现有理论结果相比，更为全面且明确，利用所得判据条件，可方便准确地对弹箭极限圆锥运动特性进行分析判断。

CHEN L , LIU R Z , GUO R , et al . Stability criteria for limiting conical motion of rotary fin-stablized projectiles [J ] . Acta Armamentarii , 2019 , 40 ( 7 ): 1329 - 1339 . (in Chinese) DOI: 10.3969/j.issn.1000-1093.2019.07.001 http://doi.org/10.3969/j.issn.1000-1093.2019.07.001 A modified theoretical model is developed to analyze the limiting conical motion characteristics of rotary fin-stablized projectiles. The amplitude plane equation of projectiles in the state of quasi-circular motion is expanded as Taylor series, by which the value change of the square-root term in the amplitude plane equation is fully considered. The existence and stability of the nonzero singular points for the amplitude plane equation are analyzed comprehensively according to the different parameter values. The analytic criteria are presented, which present the necessary conditions for the formation of stable conical motion under the action of nonlinear static moment and nonlinear Magnus moment. Furthermore, two condition expressions denoted as J₁>0 and J₂>0, which just relate to the initial parameters of the angle-of-attack equation, are claimed as the comprehensive criterions in this paper and are used for the primary analysis of conical motion stability. Finally, a rotary fin-stablized projectile with known aerodynamic and structural parameters is taken as an example to verify the theoretical critera. The results indicate that the stability criteria for the limiting Conical Motion of rotary fin-stablized projectiles proposed in this paper are more comprehensive and explicit than those of the current theory. Based on the proposed criteria, the characteristics of limiting conical motion can be analyzed and estimated conveniently and effectively. Key

舒敬荣 , 李红星 , 李宏玲 . 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 [J ] . 兵工学报 , 2018 , 39 ( 5 ): 875 - 882 . DOI: 10.3969/j.issn.1000-1093.2018.05.006 http://doi.org/10.3969/j.issn.1000-1093.2018.05.006 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。

SHU J R , LI H X , LI H L . Forced conical motion stability conditions for pneumatic eccentric projectile under the action of nonlinear moment [J ] . Acta Armamentarii , 2018 , 39 ( 5 ): 875 - 882 . (in Chinese)

吴映锋 , 钟扬威 , 王良明 . 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 [J ] . 兵工学报 , 2017 , 38 ( 7 ): 1263 - 1272 . DOI: 10.3969/j.issn.1000-1093.2017.07.003 http://doi.org/10.3969/j.issn.1000-1093.2017.07.003 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。

WU Y F , ZHONG Y W , WANG L M . Study on angular motion characteristics of spin-stabilized 2D trajectory correction projectile under the effect of fixed canards [J ] . Acta Armamentarii , 2017 , 38 ( 7 ): 1263 - 1272 . (in Chinese)

LIU Y S , LI S , LI J L . Extraction and filter algorithm of guidance information for full-strapdown seeker on rotation missile [C ] //Proceedings of MATEC Web of Conferences. EDP Sciences. Moscow, Moscow, Russia : Moscow State University of Civil Engineering (National Research University) , 2018 , 214 ( 10 ): 03008 .

DU X , XIA Q L . Research on strap-down seeker guidance information for rolling interceptor [J ] . Optik-International Journal for Light and Electron Optics , 2017 , 129 : 183 - 199 . DOI: 10.1016/j.ijleo.2016.10.042 http://doi.org/10.1016/j.ijleo.2016.10.042 https://linkinghub.elsevier.com/retrieve/pii/S0030402616312098 https://linkinghub.elsevier.com/retrieve/pii/S0030402616312098

ZIPFEL P H . Modeling and simulation of aerospace vehicle dynamics, [M ] . 3rd ed. Reston,VA,US : AIAA , 2014 .

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PARK B G . Impact angle control guidance law considering the seeker’s field-of-view limits [J ] . Proceedings of Institution of Mechanical Engineers Part G Journal of Aerospace Engineering , 2013 , 227 ( 8 ): 1347 - 1364 . DOI: 10.1177/0954410012452367 http://doi.org/10.1177/0954410012452367 http://journals.sagepub.com/doi/10.1177/0954410012452367 http://journals.sagepub.com/doi/10.1177/0954410012452367 A new optimal guidance problem with impact angle constraint and seeker’s field-of-view limits is investigated for a missile with a strapdown seeker. Impact angle control to satisfy the terminal flight path angle constraint causes missile trajectories to be very curved. Since a strapdown seeker has a narrower field-of-view than a gimbaled seeker, a missile with a strapdown seeker using the impact angle control guidance law can miss its target within the field-of-view during the homing phase, leading to the failure of the mission. Therefore, considering the seeker’s field-of-view limits is a key issue for missiles with strapdown seekers when implementing the impact angle control guidance law. To handle the seeker’s field-of-view limits in the homing guidance problem, a look angle, which is defined as the angle between the velocity vector and the line-of-sight, is considered as an inequality constraint. Based on the optimal control theory with a state variable inequality constraint, the optimal impact angle control guidance law with the seeker’s field-of-view limits is designed. The proposed guidance law is made up of three types of optimal acceleration commands: the first command is to reach the maximum look angle of the seeker, the second is to keep the seeker look angle constant on the constraint boundary, and the third is to intercept the target with the desired impact angle. Nonlinear simulations are performed to validate the proposed approach. In addition, comparisons with other guidance laws considering the limitation of the seeker look angle are carried out via nonlinear simulations, and the results show that the proposed guidance law is more efficient in terms of the control energy.

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ZHENG D , LIN D F , XU X H , et al . Dynamic stability of rolling missile with proportional navigation&PI autopilot considering parasitic radome loop [J ] . Aerospace Science and Technology , 2017 , 67 : 41 - 48 . DOI: 10.1016/j.ast.2017.03.036 http://doi.org/10.1016/j.ast.2017.03.036 https://linkinghub.elsevier.com/retrieve/pii/S1270963817305497 https://linkinghub.elsevier.com/retrieve/pii/S1270963817305497

HE S M , LIN D F , WANG J . Coning motion stability of spinning missiles with strapdown seekers [J ] . The Aeronautical Journal , 2016 , 120 ( 1232 ): 1566 - 1577 . DOI: 10.1017/aer.2016.75 http://doi.org/10.1017/aer.2016.75 https://www.cambridge.org/core/product/identifier/S0001924016000750/type/journal_article https://www.cambridge.org/core/product/identifier/S0001924016000750/type/journal_article This paper investigates the problem of coning motion stability of spinning missiles equipped with strapdown seekers. During model derivation, it is found that the scaling factor error between the strapdown seeker and the onboard gyro introduces an undesired parasitic loop in the guidance system and, therefore, results in stability issues. Through stability analysis, a sufficient and necessary condition for the stability of spinning missiles with strapdown seekers is proposed analytically. Theoretical and numerical results reveal that the scaling factor error, spinning rate and navigation ratio play important roles in stable regions of the guidance system. Consequently, autopilot gains must be checked carefully to satisfy the stability conditions.

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徐一航 , 陈少松 , 魏恺 , 等 . 正,余弦指令控制方式旋转导弹气动特性分析 [J ] . 哈尔滨工业大学学报 , 2022 , 54 ( 1 ): 114 - 122 .

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