Nonlinear model of the free-flight motion of finned bodies

The presence of large angles of attack at any stage of the flight path is a primary source of dispersion in free-flight motion of finned bodies. Nonlinear extensions of the aeroballistic theory are usually carried out with the addition of symmetry-preserving cubic terms to the linear aerodynamic coefficients. However, the roll-orientation dependence of the static yaw moment requires a better modeling. Based on the Maple–Synge expansion, a high order representation of the yaw moment is utilized to derive a simplified equation of the yawing motion, which shows good agreement with the exact solution, even with large angle-of-attack oscillations. The approximate equations can be useful to perform analytic studies on the coupled yawing and rolling motions, in particular, to determine their steady states based on nonlinear aerodynamic coefficients obtained from experimental data.