Calculation Method for the Nonlinear Angular Motion Attraction Domain of Spin-stabilized Projectile

doi:10.3969/j.issn.1000-1093.2021.06.009

Abstract

Abstract: An angular motion equation, including geometric nonlinearity and aerodynamic nonlinearity, for spin-stabilized projectile is established to calculate the attraction domain of nonlinear angular motion of projectile. The properties of the origin and its surrounding equilibrium points are analyzed, and the origin in the attraction domain is divided into non-unique stable equilibrium point and unique stable equilibrium point. For the case where the origin is non-unique stable equilibrium point, the attraction domain of the origin is obtained according to the symmetry. And for the case where the origin is the unique stable equilibrium point, the attraction domain is obtained by calculating the limit cycle radius of the subcritical Hopf bifurcation at the origin. The analysis calculation and simulation verification of a 155 mm grenade as an example were made. The results show that the proposed calculation method can be used to accurately calculate the unstable limit cycle around the origin, and the limit cycle is the boundary of attraction domain of the origin. The cubic term coefficient of Magnus moment is the main factor affecting the size of origin attraction domain; in the supersonic range, the area of the origin attraction domain first decreases and then increases with the increase in the projectile’s initial velocity. The greater the air density is, the smaller the area of the origin attraction domain is. The instability of the spin-stabilized projectiles launched from the mobile platform is also caused by the attraction domain.

Key words: spin-stabilizedprojectile, nonlinearangularmotion, attractiondomain, equilibriumpoint, subcriticalHopfbifurcation

CLC Number:

TJ012.3⁺3

YANG Zhiwei， WANG Liangming， ZHONG Yangwei， WANG Yao， ZHANG Xifeng. Calculation Method for the Nonlinear Angular Motion Attraction Domain of Spin-stabilized Projectile[J]. Acta Armamentarii, 2021, 42(6): 1195-1203.

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