Analytical Solutions for Hypersonic Glide Trajectory Based on Altitude-Velocity Profile

This article addresses the challenge of rapid trajectory planning for diverse reentry missions by introducing 3-D analytical solutions for the hypersonic glide trajectory based on the altitude-velocity profile. The 3-D analytical solutions consist of longitudinal and lateral components. For the longitudinal solutions, analytical expressions for the flight path angle and bank angle of the hypersonic glide vehicle are derived from the altitude-velocity profile. For the lateral solutions, the motion equations are simplified and subsequently transformed into solvable linear differential recurrence equations using the Newton-Raphson method. Recursive analytical solutions (RASs) are obtained by solving these equations. Meanwhile, the Chebyshev and Euler series are employed to approximate the integral terms and the exponential matrices within the RASs, resulting in approximate analytical solutions. Simulations demonstrate that the 3-D analytical solutions are rapid, efficient, and accurate, suitable for various reentry scenarios, and have broad application prospects.