The Stability Of Projectile Under Stochastic Disturbance

The main reserch of this article is the stability characteristic of projectiles in flight under random disturbance. According to the mass center motion equations and the rotational motion equation, the simplified angle motion equation of projectile was established. By using the Runge-Kutta method, the stability of determine projectile system was simulated and analyzed, then the dynamics behavior of stochastic missiles system was simulated combined with Monte Carlo method and maximum Lyapunov index method. And the dynamics behavior differences of projectile angle motion system were given before and after the introduction of random noise.This article summarized the research status of the stability of projectiles in flight at home and abroad firstly, introduced the importance of adding random noise into the stability analysis of projectile stability. Then the stochastic dynamics analysis was given of the basic theories and methods. Combined with numerical simulation and theoretical analysis, it probed into the random noise system dynamics behavior changes before and after the intervention of noise. In numerical analysis part, according to the characteristic value, probability density function of the bifurcation diagram and the largest Lyapunov exponent, the stability characteristics were researched before and after the intervention of random disturbance signal. The main characteristics of the stability of the rocket was studied under different environmental density and speed respectively. The unstable points, limit cycles and bifurcation points in both cases were showed in the figures, and through the maximum Lyapunov exponent, the types of the bifurcation point were determined. The dynamics behavior characteristics was obtained under different density and speed with random disturbance, and the effects of density on stability was analyzed.Finally, the projectile system was reduced adopting the method of random center manifold reduction and its random response problems were studied. By solving the analytical solution of the transfer probability density function of missiles system, the random response was obtained, which helps to quantitatively analyze the stability and other random dynamic behavior of projectile system.The results of numerical analysis provided a theoretical support to a certain extent for the projectile stability research and design, and provided a certain reference basis to solve the stability problem of projectile system with random noise. The analysis method adopted also has a certain application value.