Okhotsimsky-Egorov Method for Solving the Euler-Lambert Problem

A method for solving the Euler-Lambert problem by V.A. Egorov is presented, based on the work of D.E. Okhotsimsky and on the analysis of a set of orbits for а flight between two given positions in the central Newtonian field. The method allows to find the orbit of the flight for a given time. The unknown parameter of the orbit is set in the initial flight-path angle. The advantages of this method include the explicit dependence of the solution on the speed inclination at the starting point, as well as the limited range of the angle of inclination of the speed. Solutions of the Euler-Lambert problem with a given number of revolutions are given as an example, the effectiveness of the developed method is compared to known methods. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.