Elastic deformation modeling of the VS-40M suborbital rocket with SARA payload

The aim of this paper is to present the flight dynamics analysis developed to the suborbital rocket VS-40 with SARA (Atmospheric Reentry Satellite) payload by taking into account the elasticity of the launcher in the equations of dynamics. The way to include structural dynamics in such an approach is the main topic of this paper. In order to include the flexibility in the overall dynamic analysis of the launcher, a mathematical model of a fully flexible structure subjected to thrust, aerodynamic and gravity forces is presented. By opportunely writing the translational, rotational and flexible dynamic equations, it is possible to obtain a fully non-linear system of equations of motion where the roles of the macro dynamics (representative of the translational and rotational flight mechanics of the launcher) and the micro dynamics (elastic vibrations) can be clearly appreciated. The elastic displacement of the launcher is represented through the modal superposition technique whereas the micro dynamics effects are obtained via Galeerkin approach. The consistency of the results, modal parameters and the trajectory of the launcher are checked by comparison with its rigid body trajectory obtained from a qualified trajectory code.