Analytical trajectory prediction for near-first-cosmic-velocity atmospheric gliding using a perturbation method. (October 2021) - Yu, Wenbin; Yang, Jin; Chen, Wanchun; Liao, Bo; Zhu, Hengwei
Abstract: 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. Highlights: This glide problem is special as the speed is close to the first cosmic velocity. 3-D analytical trajectory solutions are derived based on the drag profile. The coupling of longitudinal and lateral differential equations is fully considered. Some difference expressions are created to weaken the effect of coupling terms. Two analytically solvable sub-systems are developed by a perturbation method.