Reconstructing the Equations of Motion of Atmospheric Entry Vehicle Using High-Order Approach

A blunt body entering through the atmosphere is subjected to strong forces and moments, which can lead to strong oscillations in the trajectory. Therefore, it is important to identify these oscillations and analyze the dynamic motion of the vehicle for a safe entry and descent. However, this challenging event includes complex interactions of the vehicle with wake flow, compression wave, and shear layer. To that end, a simplified model is derived and used in literature to identify the dynamic stability of the vehicle. However, the simplified model is a first-order approach where the relation of the trajectory with the pitch-damping and pitching rate derivatives is neglected. In the present study, a theoretical approach is developed to incorporate the relation of the high-order that helps capture more physical information. Thus, a system dynamics discovery model based on SINDy and MCMC-NUTS is used to reconstruct equations of motions and estimate the dynamical derivatives. SINDy framework is utilized to discover the governing equations. However, the coefficients of the discovered equations are numeric without a physical connection to the aerodynamic derivatives, so the MCMC-NUTS algorithm is used to infer these numeric values into the theoretical high-order approach to complete the physical model. Initially, synthetic data based on a second-order approach will be used. Then, the contribution of high-order terms will be investigated for different release angles. Finally, the proposed model will be verified through an inverse problem to recover the governing equations using the SINDy algorithm and the distribution of the estimated coefficients using the MCMC-NUTS Bayesian inference tool.