Mathematical Model of the Rotational Motion of a Sounding Rocket with Aerodynamic Rudders

Mathematical models are developed for the moments of control forces produced by aerodynamic rudders, assuming that the rocket's angular stabilization system ensures the necessary precision of angular stabilization. It is demonstrated that under these conditions, the rocket's rotational motions along the yaw, pitch, and roll channels can be effectively treated as independent of each other for engineering calculations. The equations governing the rotational motion of a sounding rocket equipped with four aerodynamic rudders are derived, along with formulas for computing the aerodynamic forces and moments generated by the rudders and stabilizers. Furthermore, the equations of motion for the rocket’s angular stabilization system concerning the pitch angle are formulated, and the region of its asymptotic stability within the control law parameter space is delineated. A numerical simulation is conducted to analyze the dynamics of the pitch angle stabilization system in an experimental model rocket, showcasing the efficacy of the coefficient method for assessing the stability of the rocket’s angular stabilization system.