Integrated Development of the Equations of Motion for Elastic Hypersonic Flight Vehicles

Abstract

An integrated, consistent analytical framework is developed for modeling the dynamics of elastic hypersonic flight vehicles. A Lagrangian approach is used to capture the dynamics of rigid-body motion, elastic deformation, fluid flow, rotating machinery, wind, and a spherical rotating Earth model and to account for their mutual interactions. The resulting equations of motion govern the rigid-body and elastic degrees of freedom (DOF). The elastic motion is represented in terms of modal displacement coordinates relative to the elastic mean axes system, and the rigid-body motion is represented in terms of the translational and rotational velocities of this axes system. A vector form of the force, moment, and elastic-deformation equations is developed from Lagrange's equation; a usable scalar form of these equations is also presented. The appropriate kinematic equations are developed and are presented in a usable form. The characteristics of the three-DOF point-mass dynamic model are also outlined, and the corresponding equations are presented. A preliminary study of the significance of selected terms in the equations of motion is conducted. Using generic data for a single-stage-to-orbit vehicle, it was found that the Coriolis force can reach values up to 6 % of the vehicle weight and that the forces and moments attributable to fluid-flow terms can be significant.