Longitudinal Rigid Body and Flexible Body Simulation Models for Air-Breathing Hypersonic Vehicles

Longitudinal motion simulation of hypersonic vehicles typically requires consideration of two distinct modeling approaches: rigid body models and flexible body models. These models describe the vehicle's dynamic characteristics under different conditions, providing critical foundations for engineering design and analysis.

The rigid body model assumes no deformation during vehicle motion, primarily focusing on center-of-mass movement and rotation about the mass center. This simplified approach is suitable for preliminary design and rapid simulations, effectively capturing fundamental dynamics such as pitch rate and angle of attack variations. In implementation, this typically involves solving Newton-Euler equations using numerical integration methods like Runge-Kutta algorithms within Simulink S-functions.

The flexible body model incorporates potential structural elastic deformations that may occur during hypersonic flight. Given that hypersonic vehicles often feature slender body configurations, aerodynamic heating and complex loading conditions can induce significant elastic effects that impact stability and control performance. This model employs modal coordinates and structural dynamics equations through finite element method implementations, enabling more accurate prediction of actual vehicle behavior. The implementation typically involves coupling aerodynamics with structural modes using state-space representations.

Developing simulation modules for both models using Simulink S-functions leverages MATLAB/Simulink's robust numerical computation and visualization capabilities. By comparing simulation results from both approaches, engineers can gain deeper insights into how elastic effects influence vehicle performance, providing valuable references for control system design and optimization. The S-function implementation allows for custom algorithms including real-time parameter updates and multi-rate sampling techniques for efficient simulation.