宇航学报 ›› 2020, Vol. 41 ›› Issue (4): 398-409.doi: 10.3873/j.issn.1000-1328.2020.04.003

• 飞行器设计与力学 • 上一篇    下一篇

单通道控制旋转弹系统动力学建模与Hopf分岔

许艳丽,岳宝增,赵良玉   

  1. 北京理工大学宇航学院, 北京 100081
  • 收稿日期:2019-05-08 修回日期:2019-07-05 出版日期:2020-04-15 发布日期:2020-04-25
  • 基金资助:
    国家自然科学基金(11472041,11772049,11532002,11802320)

Dynamical Modeling and Hopf Bifurcation for the Coning Motion of Spinning Missiles under Single Channel Control#br#

XU Yan li, YUE Bao zeng, ZHAO Liang yu   

  1. School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
  • Received:2019-05-08 Revised:2019-07-05 Online:2020-04-15 Published:2020-04-25

摘要: 为准确预测旋转弹系统的锥形运动形态并判断其稳定性,提出一对鸭舵引起的气动不对称性以及可能引起复杂非线性动力学特性的非线性因素,建立能准确描述单通道控制旋转弹系统姿态运动的复数形式的动力学模型并分析讨论其动态稳定性条件。利用分岔理论对单通道控制旋转弹系统开展Hopf分岔研究,给出了Hopf分岔发生的判断准则;推导了用于判定极限环稳定的第一Lyapunov系数。数值仿真结果验证了条件的正确性与有效性并发现了拟周期运动及混沌运动。研究结果为旋转弹的控制参数设计及结构参数设计提供理论参考。

关键词: 非线性旋转弹, 稳定性, Hopf分岔, 拟周期运动, 混沌运动

Abstract: To accurately predict the coning motion forms of a rolling projectile system and determine their stability, the complex dynamic model is established and its analytical conditions for motion stability are presented in consideration of the aerodynamic asymmetry caused by a pair of canards and nonlinear factors. The Hopf bifurcation analysis is carried out for the single-channel rolling system by using bifurcation theory. The analytic conditions for the occurrence of the Hopf bifurcation are presented and the first Lyapunov coefficients are also derived analytically to determine the stability of the limit cycles. Numerical simulations confirmed the validity of the presented conditions and the existence of quasi periodic motion and chaotic motion. The results given in this paper will contribute to the theoretical references for the design of the control parameters and the structure parameters in the engineering practices.

Key words: Nonlinear rolling projectile, Stability;Hopf bifurcation;Quasi periodic motion;Chaotic motion

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