Analytical Solutions to Aeroassisted Orbital Transfer Problem
Wenbin Yu, Penglei Zhao, Wanchun Chen
Abstract
In this article, the atmospheric flight of aeroassisted orbit transfer vehicle is investigated analytically. As the flight speed is greater than the first cosmic velocity, the centrifugal force is also larger than gravity. Due to this, the vehicle has to fly with a downward lift and the flight altitude is extremely unstable. To cope with this challenge, the high-precision formulae of altitude and flight-path angle for steady glide are deduced and used to develop the steady glide control technique to stabilize the flight altitude. Upon steady glide, the analytical solutions for 3-D aeroassisted maneuvering trajectory are derived. In the derivation, a reduced-order system with negative lift-to-drag ratio as control variable is obtained by subtly simplifying the nonlinear flight dynamics. To address the complex influence of Coriolis force, the regular perturbation method is used such that the system is further decomposed into two special linear time-varying systems, which can be solved analytically by the spectral-decomposition-based method. Due to the full consideration of the influence of the Earth's curvature and rotation, the analytical solutions can predict the downrange, crossrange, and heading angle of the 3-D trajectory accurately.