Solution of the Euler–Lambert Problem Based on the Okhotsimsky–Egorov Ballistic Approach

Abstract

The paper propose the method for solving the Euler–Lambert problem proposed by V.A. Egorov and based on the works by D.E. Okhotsimsky, devoted to the analysis of a set of flight trajectories between two given points in the central Newtonian field. When considering the Euler–Lambert problem as the inverse problem of ballistics (dynamics), we have succeeded in developing a new effective method for determining the orbit corresponding to a given flight time. It is logical to name this approach the Okhotsimsky–Egorov method. In the considered approach, the parameter of the set of flights is the initial flight-path angle. The advantages of the proposed method are the limited and understandable structure of the domain of definition of solutions, the simplicity and clarity of the algorithm, and the clear dependence of the solution on the initial velocity. It enables a qualitative analysis of flight trajectories and the construction of effective numerical methods. To solve the Euler–Lambert problem Halley’s numerical method was used. A computational complexity analysis of considered algorithm was carried out and demonstrated its high efficiency.