Lateral Stability Analysis of Hypersonic Vehicle under Pressure Fluctuation by Solving Mathieu Differential Equation

TL;DR

This paper investigates the impact of pressure fluctuations on the lateral stability of hypersonic vehicles, modeling the problem with Mathieu differential equations to highlight potential failure mechanisms and inform control strategies.

Contribution

It introduces a novel approach by modeling hypersonic vehicle lateral stability with pressure fluctuations using Mathieu equations, emphasizing their significance in stability analysis.

Findings

Pressure fluctuations significantly affect lateral stability.

Mathieu differential equation models the dynamic response.

Fluctuations lead to complex stability behavior.

Abstract

Two recent test failures of Hypersonic Technology Vehicle 2 impose a strike to the increasingly growing enthusiasm, not only on the United States side. It is important to find out the exact failure reason, otherwise a solution is impossible. In this Note, we propose a potential failure reason from the perspective of lateral stability analysis. We argue that the time variant pressure fluctuations, which are normally omitted in classical aircraft dynamics analysis, could not be neglected in dynamic analysis of hypersonic vehicles. To demonstrate the idea, a hypersonic model is imagined in this work and its aerodynamic parameters are estimated using fundamental fluid principles. Pressure fluctuations are thereafter estimated by an empirical formula. A lateral dynamic equation is set up, taking those time variant fluctuations into account. The resulted equation is a Mathieu differential equation. Numerical solutions of this equation show that the inclusion of fluctuation terms generates more complicated dynamics and should be considered in flight controller design.