Journal of Astronautics ›› 2020, Vol. 41 ›› Issue (4): 398-409.doi: 10.3873/j.issn.1000-1328.2020.04.003

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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

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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