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<p>Obtaining analytical solutions is usually intractable due to the highly nonlinear and coupled nature of hypersonic glide dynamics in tracking, controlling and navigating fields. The purpose of this paper is to seek novel analytical expressions of equilibrium glide solutions (EGS) under decoupled elementary functions, theoretically. The analytical expression for the initial value of the flight path angle is firstly deduced by adopting the mean value theory. Based on the equilibrium glide condition, new analytical forms of EGS for state variables are derived with the help of scaling methods and new variables during derivations. Correction method for EGS is proposed to avoid singularity after the critical point. The effectiveness of EGS is verified with the classical 4th-order Runge–Kutta method under various reentry conditions. EGS has clear physical meaning, and demonstrates better performance than other recent analytical solutions. The MEAE of geocentric radius and velocity is lower than 3.20&#xa0;km and 181.39&#xa0;m/s. The results of EGS can provide references and data support for trajectory prediction and rapid design of equilibrium glide vehicles.</p>

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Novel Simplified Analytical Methods for the Hypersonic Equilibrium Glide Dynamics

  • 期刊论文

  • 发表日期：

    2025年11月4日

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  • Yuanjie Qi,
  • Yan Zhang,
  • Jintao Chen,
  • Kun Huang,
  • Zhuangbin Tan

摘要

Obtaining analytical solutions is usually intractable due to the highly nonlinear and coupled nature of hypersonic glide dynamics in tracking, controlling and navigating fields. The purpose of this paper is to seek novel analytical expressions of equilibrium glide solutions (EGS) under decoupled elementary functions, theoretically. The analytical expression for the initial value of the flight path angle is firstly deduced by adopting the mean value theory. Based on the equilibrium glide condition, new analytical forms of EGS for state variables are derived with the help of scaling methods and new variables during derivations. Correction method for EGS is proposed to avoid singularity after the critical point. The effectiveness of EGS is verified with the classical 4th-order Runge–Kutta method under various reentry conditions. EGS has clear physical meaning, and demonstrates better performance than other recent analytical solutions. The MEAE of geocentric radius and velocity is lower than 3.20 km and 181.39 m/s. The results of EGS can provide references and data support for trajectory prediction and rapid design of equilibrium glide vehicles.