NONLINEAR FLIGHT DYNAMIC ANALYSIS OF BLUNT BODY ENTRY VEHICLES USING MULTIPLE TIME SCALES METHOD

Abstract

Atmospheric entry is a critical phase for mission that seeks to return astronauts or scientific payloads back to Earth or explore the surface of a planet with an appreciable atmosphere. This project aims at the comprehensive investigation of the dynamic stability of blunt body atmospheric entry vehicles. As blunt vehicle enters a planetary atmosphere, the aerodynamic moments acting upon it can result in unstable pitching motions and divergence of oscillation amplitude. Typically, these instabilities are found in the low or mid supersonic regime of the trajectory just prior to parachute deployment. The amplitude envelope of a planetary probe as it enters an atmosphere can play an important role in terminal events like the deployment of parachutes and entry/reentry trajectories. Most analysis considers the case of constant or linear aerodynamic coefficients. In many cases the aerodynamic coefficients exhibit nonlinear behavior. In this research, the nonlinearities of various stability coefficients are correlated with the system response by generating approximate closed form analytical solutions. For this purpose, the Multiple Time Scales method in conjunction with bifurcation theory is used to obtain the approximate solutions of the multiple degree-of-freedom nonlinear equations of motion. The explicit analytical results obtained are useful to identify the key parameters affecting the dynamics and stability of the blunt body atmospheric entry vehicle. The conditions leading to limit cycle responses in the vicinity of loss of damping regime are discussed. The analytical solution is duly validated with the numerical solution in the end. Such research endeavors will help the Government of Pakistan to realize the goals of “Space Programme 2040” and bring the benefits of the complete spectrum of space technology to the people of Pakistan.