Extension of the second-order theory of entry mechanics to nearly exact solutions.

Abstract

The fundamental equations of entry at constant lift-drag (L/D) ratio are not solvable analytically. However, by restricting the equations in a limited region of application, several first-order approximate analytical solutions were obtained in the last few years. These firstorder solutions include those of Gazley, Alien and Eggers, Chapman, Lees, Ting, Loh, and Arthur. For variable L/D ratio, where the L/D ratio can be varied in a specified way, Loh's exact analytical solutions are available. Later, a second-order solution of entry mechanics was developed by Loh. Although this second-order solution is valid for the entire entry region, and it can be reduced either analytically or numerically to all the first-order solutions mentioned previously, it is limited to nonoscillatory-type entry trajectories. So far, oscillatory-type trajectories can only be solved by electronic computers. Recently, Loh's extension of the second-order solution for application to both circular and supercircular oscillatorytype entry trajectories was made. However, the extension was made for skip-out-of-the atmosphere-type oscillating trajectories. For oscillating trajectories which are completely within the atmosphere, a further extension of the second-order solution is presented in this paper.