A Complex Variable Method to Predict a Range of Arbitrary Shape Ballistic Projectiles

Abstract

This paper considers a mariner under PDμ controller and analyses the effects of controller parameters on the yaw rate by using the Nomoto model. The Nomoto model describing the time evolution of the yaw rate of the steering dynamics of a mariner is reduced to an asymmetric Duffing oscillator with fractional order derivative. Under the approximation of calm water, the steady behavior of the mariner shows an “imperfect” supercritical pitchfork bifurcation. Region of safe behavior is identified and strategy to reduce the yaw rate by an appropriated selection of controller parameters are discussed. The frequency analysis of the mariner shows the prominence of hysteresis is reduced for small order of the fractional derivative as well as the amplitude of the yaw rate. Evidence of chaotic response is illustrated using robust chaotic indicators such as the Lyapunov exponent and the fast Fourier transform.