This paper investigates a special atmospheric glide problem where the gliding speed is close to the first cosmic velocity (FCV). Here, the centrifugal force and gravity almost balance each other, and thus in the local vertical direction the lift force required to maintain the glide is almost zero. However, all the existing analytical solutions for 3-D gliding trajectories were derived under the condition that the vertical component of lift is large enough, and thus become invalid for the special glide case. To overcome the shortage of the existing studies, we abandon the vertical component of lift, but instead plan the profile of drag acceleration (a_D) to derive the analytical solutions for the 3-D special gliding trajectory. By simplifying the nonlinear equations of motion properly, a reduced-order system is obtained and governed by a_D and L₂/D, where L₂/D represents the ratio of the local horizontal component of lift to drag. Subsequently, by proposing a perturbation method to expand the system in Taylor series with finite terms, two analytically solvable subsystems are developed. As a result, the analytical trajectory solutions are obtained successfully. Additionally, as verified by the simulation results, the new solutions are also applicable to the conventional glide problem where the speed is much less than the FCV, and found to be much more accurate than the existing solutions because the new solutions give full consideration to the coupling of the longitudinal and lateral equations.

本文研究了一个特殊的大气滑翔问题，其中滑翔速度接近第一宇宙速度（FCV）。在这里，离心力和重力几乎相互平衡，因此在局部垂直方向上，维持滑翔所需的升力几乎为零。然而，现有的3-D滑翔轨迹解析解都是在升力的垂直分量足够大的情况下推导出来的，因此对于特殊的滑翔情况是无效的。为了克服现有研究的不足，我们放弃了升力的垂直分量，而是规划了阻力加速度的剖面（a _D) 推导出 3-D 特殊滑翔轨迹的解析解。通过适当地简化运动的非线性方程，得到降阶系统并受一个_d和L ₂ / d，其中L ₂/D 表示升力与阻力的局部水平分量之比。随后，通过提出一种微扰方法来扩展具有有限项的泰勒级数系统，开发了两个可解析解的子系统。结果，成功地获得了解析轨迹解。此外，通过仿真结果验证，新的解决方案也适用于速度远小于 FCV 的常规滑翔问题，并且发现比现有的解决方案准确得多，因为新的解决方案充分考虑了纵向和横向方程的耦合。