Title: Asymptotic stabilisation of motion on circular intermediate thrust arcs in a field of two fixed centres

Authors: Natalya Korshunova; Dilmurat Azimov

Addresses: Department of Theoretical and Applied Mechanics, National University of Uzbekistan, Tashkent, 7000174 Vuz Gorodok, Uzbekistan ' Mechanical Engineering, University of Hawaii at Manoa, 2540 Dole Street, Holmes 202A, 96822 Honolulu, Hawaii, USA

Abstract: The variational problem of minimising the characteristic velocity of motion in a gravitational field of two fixed centres is considered. It is shown that if a cylindrical coordinate system with the origin at one of the fixed centres is introduced, then the differential equations of motion on circular intermediate thrust arcs are analytically integrable using the method of Levi-Civita and particular analytical solutions can be formulated. The controllability at the first approximation and asymptotic stability of an unperturbed motion on such arcs can be achieved by changing only the transversal component of the thrust vector. Illustrative example is presented.

Keywords: variational problem; trajectory optimisation; two fixed centres; asymptotic stability; analytical solution; intermediate thrust arc.

DOI: 10.1504/IJSPACESE.2017.085648

International Journal of Space Science and Engineering, 2017 Vol.4 No.3, pp.167 - 173

Received: 11 Aug 2016
Accepted: 29 Aug 2016
Published online: 05 Aug 2017 *

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