Elastic Dynamic Effects on the Trajectory of a Flexible Launch Vehicle

Abstract

This paper explains the full process of calculating the trajectory and vibration characteristics of a spinning flexible launch vehicle. The rigid and elastic coupled equations of motion are derived using the Lagrangian approach. The transfer matrix method of linear multibody system dynamics is used to evaluate the vehicle’s natural frequencies and bending mode shapes, which vary with time in the boosting phase of flight. The vehicle is idealized as a nonuniform beam with variable mass and stiffness distributions with thrust and mass depleting effects accounted for. The aerodynamic loads on the vehicle are obtained through the slender-body aerodynamic derivatives method based on quasi-steady theory. Because of thrust effect in the boosting phase, the vehicle experiences larger deformations than at burnout. Different mode orders and zero structural damping are applied respectively, which leads to the conclusion that the flexible vehicle’s vibration is basically a function of the fundamental mode, and structural damping may be ignored. The deformation of an elastic rocket may diminish the static margin, increasing the pitch angle and reducing the yaw angle compared to a rigid vehicle. These factors and the elastic-body local angle of attack influence the vehicle’s flexible motion and should not be neglected.