Analytical solution for three-dimensional skip re-entry trajectory

Accurate and efficient prediction of three-dimensional skip re-entry trajectories is essential for trajectory planning and guidance of reusable spacecraft, yet the strongly nonlinear dynamics have hindered the investigation of practical closed-form solutions. This paper aims to derive high-accuracy, computationally efficient analytical solutions for large-span, three-dimensional skip trajectories of hypersonic re-entry vehicles. To overcome the difficulty, a generalized dynamic model with kinetic energy as the independent variable is developed and decomposed into several analytically solvable subsystems by proposing a perturbation method and introducing auxiliary altitude and flight path angle. The subsystem for speed, altitude, and flight path angle is solved first, and then the solutions for the generalized longitude, latitude, and heading angle are derived. Simulation results demonstrate that the new method improves position and velocity prediction accuracy by an average of 52 % and 19 %, respectively, compared to existing solutions for skip re-entry trajectories. Moreover, the new solutions exhibit high computational efficiency, with an average runtime of only about 0.08 ms.