Analytical trajectory solutions for atmospheric pull-up phase of interplanetary return flight. (April 2022) - Yu, Wenbin; Yang, Jin; Chen, Wanchun; Zhu, Hengwei
Abstract: As a study on the flight of an interplanetary spacecraft back to Earth, the approximate analytical solutions for the atmospheric trajectory from reentry interface to pull-up point are derived. In future research, the solutions will be used as the theoretical tools for designing an analytical predictor-corrector guidance algorithm to control the pull-up flight. To derive the solutions, the highly nonlinear reentry dynamics is simplified first by planning the profile of drag-coefficient as an inversely proportional function of energy and using atmospheric density as a new state variable to replace altitude. Then, in order to decouple the dynamical equations, reference atmospheric density and reference flight-path angle are introduced to replace some real state variables while the differences between the reference and real variables are treated as small perturbations. Finally, a perturbation method is proposed to decompose the dynamics into two analytically solvable sub-systems. Thus the approximate analytical solutions are derived successfully. The simulation results demonstrate that the new solutions are more accurate than the existing solutions, because the new solutions give full consideration to the influence of Earth's curvature and rotation. Highlights: Analytical trajectory solutions for atmospheric pull-up phase of interplanetary return flight are derived. A novel flight dynamics is proposed by taking atmospheric density as a state variable. Drag coefficient is planned skillfully as an inversely proportional function of energy. The flight dynamics is decoupled by introducing some reference state variables. The decoupled dynamics is decomposed into two analytically solvable subsystems by a perturbation method.