Solution algorithm of a quasi-Lambert’s problem with fixed flight-direction angle constraint
Source: Celestial Mechanics and Dynamical Astronomy, Volume 109, Number 4, April 2011 , pp. 409-427(19)
Abstract:A two-point boundary value problem of the Kepler orbit similar to Lambert’s problem is proposed. The problem is to find a Kepler orbit that will travel through the initial and final points in a specified flight time given the radial distances of the two points and the flight-direction angle at the initial point. The Kepler orbits that meet the geometric constraints are parameterized via the universal variable z introduced by Bate. The formula for flight time of the orbits is derived. The admissible interval of the universal variable and the variation pattern of the flight time are explored intensively. A numerical iteration algorithm based on the analytical results is presented to solve the problem. A large number of randomly generated examples are used to test the reliability and efficiency of the algorithm.
Document Type: Research Article
Affiliations: 1: Beijing University of Aeronautics and Astronautics, Xue Yuan Road No. 37, HaiDian District, 100191, Beijing, China, Email: firstname.lastname@example.org 2: China Academy of Space Technology, 5142 Mail Box, 92 sub Mail Box, 100094, Beijing, China, Email: email@example.com 3: Beijing University of Aeronautics and Astronautics, Xue Yuan Road No. 37, HaiDian District, 100191, Beijing, China, Email: firstname.lastname@example.org
Publication date: 2011-04-01