Modeling and Stability Analysis of Coning Motion for Spinning Missiles

JIANG Yuening; LI Xixi; MA Guangfu; LEI Zihan; ZHANG Deping; ZHANG Ao

doi:10.15892/j.cnki.djzdxb.2025.05.007

Journal of Projectiles, Rockets, Missiles and Guidance >

2025 , Vol. 45 >Issue 5: 642 - 647

DOI: https://doi.org/10.15892/j.cnki.djzdxb.2025.05.007

Academic article

Modeling and Stability Analysis of Coning Motion for Spinning Missiles

JIANG Yuening ,
LI Xixi ,
MA Guangfu ,
LEI Zihan ,
ZHANG Deping ,
ZHANG Ao

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Sichuan Aerospace System Engineering Research Institute, Chengdu 610100, China

Received date: 2024-10-22

Online published: 2025-11-28

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Abstract

In order to study the spinning projectile stability of coning motion,provide the dynamic equation around the center of mass in quasi-body coordinate system and establish the short period dynamic model.Derive the equations of coning motion represented by Euler angles.Obtain the analytical solution by introducing complex angle of attack.Analyze the stability of coning motion with initial disturbance in two cases:One situation is ignoring the Magnus effect and damping effect,only analyze the coning motion influenced by the gyroscope effect and the aerodynamic static moment.Another situation is the coning motion adding in the Magnus effect and damping effect,analyze the stabilization and provide the conditions for coning stability.Finally,summarize the influence of rotating speed and statically stability acting on the dynamic stability of coning motion based on theoretical analysis and simulation results:For the low-speed rotating missiles,only under the influence of gyroscopic effect and aerodynamic static moment,a statically stable aerodynamic shape is necessary to achieve coning stability.Statically unstable missiles can only achieve dynamic stability by significantly increasing the rotating speed.Considering the Magnus effect and damping effect,the convergent coning motion of the statically stable missiles with low rotating speed is the easiest to achieve.The divergence of coning motion may occur result in the increasing of rotating speed.For the statically unstable missiles,it is necessary to select the moment of inertia reasonably and increase the rotating speed to achieve dynamic stability.

Key words： spinning missiles; coning motion; dynamic stability; attitude dynamic model; gyroscopic effect; statically stability; statically instability

Cite this article

JIANG Yuening , LI Xixi , MA Guangfu , LEI Zihan , ZHANG Deping , ZHANG Ao . Modeling and Stability Analysis of Coning Motion for Spinning Missiles[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2025 , 45(5) : 642 -647 . DOI: 10.15892/j.cnki.djzdxb.2025.05.007

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References

Publishing order | Descend order by publishing year | Descend order by cited within

[1]	Peterson V L, Schiff L B, Tobak M. Aerodynamics of bodies of revolution in coning motion[J]. AIAA Journal, 1969, 7(1):95-99. DOI

[2]	钱杏芳, 林瑞雄, 赵亚男. 导弹飞行力学[M]. 北京: 北京理工大学出版社, 2008. QIAN X F, LIN R X, ZHAO Y N. Missile flight dynamics[M]. Beijing: Beijing Institute of Technology Press, 2008.

[3]	周伟. 旋转弹动态稳定性与鲁棒变增益控制[D]. 北京: 北京理工大学, 2016. ZHOU W. Dynamic stability and robust gain-scheduling control of spinning missiles[D] Beijing: Beijing Institute of Technology, 2016.

[4]	李克勇, 赵良玉, 周伟. 一类旋转弹在高空中的锥形运动稳定性[J]. 动力学与控制学报. 2012, 10(3):239-243. LI K Y, ZHAO L Y, ZHOU W. Stability of coning motion of spinning rocket projectiles at high altitude[J]. Journal of Dynamics and Control. 2012, 10(3):239-243.

[5]	颉凯平, 畅仲仁, 郑书娥. 火箭弹发射试验锥形运动稳定性分析[J]. 弹箭与制导学报. 2016, 36(4):44-46. DOI XIE K P, CHANG Z R, ZHENG S E. Stability analysis of conical motion for rocket launching test[J]. Journal of Projectiles,Rockets,Missiles and Guidance. 2016, 36(4):44-46.

[6]	贾宝, 薛林, 闫晓勇. 自旋导弹飞行共振稳定性研究[J]. 固体火箭技术. 2015, 38(1):23-29. JIA B, XUE L. YAN X Y. Analysis of resonance stability for spinning missile[J]. Journal of solid rocket technology. 2015, 38(1):23-29.

[7]	高庆丰. 旋转导弹飞行动力学与控制[M]. 北京: 中国宇航出版社, 2016. GAO Q F. Flight dynamics and control of spinning missiles[M]. Beijing: China Astronautic Publishing House, 2016.

[8]	段笑菊, 孙瑞胜, 白宏阳, 等. 锥形运动控制的导弹姿态稳定性分析[J]. 国防科技大学学报, 2015, 37(3):97-103. DUAN X J, SUN R S, BAI H Y. Analysis on the altitude stability of missile with coning motion-based control[J]. Journal of National University of Defense Technology. 2015, 37(3):97-103.

[9]	雷娟棉, 吴甲生. 尾翼稳定大长径比无控旋转火箭弹的锥形运动与抑制[J]. 空气动力学学报, 2005, 23(4):455-457. LEI J M, WU J S. Coning motion and restrain of large fineness ration unguided spinning rocket stabilized with tail fin[J]. Acta Aerodynamic Sinica[J]. 2005, 23(4):455-457.

[10]	Murphy C H. Symmetric missiles dynamic instabilities[J]. Journal of Guidance,Control,and Dynamics. 1981, 4(5):464-471.

[11]	Murphy C H. Nonlinear motion of a missile with slight configurational asymmetries[J]. Journal of Spacecraft and Rockets, 1971, 8(3):259-263. DOI

[12]	Schiff L B. Nonlinear aerodynamics of bodies in coning motion[J]. AIAA Journal, 1972, 10(11):1517-1522. DOI

[13]	Platus D H. Missile and spacecraft coning instabilities[J]. Journal of guidance,control,and dynamics. 1994, 17(5):1011-1018. DOI

[14]	Platus D H. Ballistic re-entry vehicle flight dynamics[J]. Journal of Guidance,Control,and Dynamics, 1982, 5(1):4-16. DOI

[15]	闫晓勇, 杨树兴, 张成. 基于章动运动理论的火箭弹锥形运动稳定性分析[J]. 兵工学报, 2009, 30(10):1291-1296. YAN X Y, YANG S X, ZHANG C. Analysis of stability for coning motion of rockets based on theory of nutation movement[J]. Acta Armamentarii, 2009, 30(10):1291-1296.

[16]	王华毕, 吴甲生. 火箭弹锥形运动稳定性分析[J]. 兵工学报. 2008, 29(5):562-566. WANG H B, WU J S. The coning motion stability analysis of rocket[J]. Acta Armamentarii, 2008, 29(5):562-566.

[17]	陈尔康, 廖欣, 高长生, 等. 旋转导弹喷气阻尼效应建模与分析[J]. 哈尔滨工业大学学报, 2018, 50(10):42-48. CHEN E K, LIAO X, GAO C S, et al. Modeling and analysis of jet damping effect for spinning missiles[J]. Journal of Harbin Institute of Technology, 2018, 50(10):42-48.

[18]	廖欣, 陈尔康, 高长生, 等. 喷气阻尼效应作用下旋转导弹锥形运动分析[J]. 上海航天, 2017,34:29-35. LIAO X, CHEN E K, GAO C S. Analysis of coning motion for rolling airframe missiles under jet damping effect[J]. Aerospace Shanghai, 2017,34:29-35.

[19]	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.

[20]	韩子鹏. 弹箭外弹道学(第2版)[M]. 北京: 北京理工大学出版社, 2022. HAN Z P. Exterior Ballistics of Projectiles and Rockets(2nd edition)[M]. Beijing: Beijing Institute of Technology Press, 2022.

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