The asymptotic properties of the motions of satellites in a central field due to internal dissipation |
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| Authors: | NI Amel’kin |
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| Institution: | 1. Department of Computer Engineering, Biruni University, Istanbul, Turkey;2. Federal University Dutse, Science Faculty, Department of Mathematics, Jigawa 7156, Nigeria;3. Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia;4. Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan;5. Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy;1. Laboratory of Applied Mathematics, DICAM, University of Trento, Trento, Italy;2. Escuela Universitaria de Ingeniería Mecánica, Universidad de Tarapacá, Arica, Chile;3. Clean Combustion Research Center, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia;1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, China;2. Department of Mechanical Engineering, The University of Auckland, Auckland, 1010, New Zealand;1. School of Engineering, Robert Gordon University, Garthdee Road, Aberdeen AB10 7GJ, UK;2. Centre for Applied Dynamics Research, School of Engineering, King?s College, University of Aberdeen, Aberdeen AB24 3UE, UK;3. State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 200240, PR China;1. Department of Civil Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia;2. Department of Building Survey, Faculty of Built Environment, University of Malaya, 50603 Kuala Lumpur, Malaysia;3. Center for Building, Construction & Tropical Architecture (BuCTA), Faculty of Built Environment, University of Malaya, 50603 Kuala Lumpur, Malaysia |
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| Abstract: | A satellite in the form of a system of bodies that does not have the property of a gyrostat in the general case is considered. An algorithm for determining all the equilibrium configurations of the system that correspond to steady motions in a central gravitational field and an algorithm for analysing their stability are given. A method based on Routh's first theorem is used to investigate the asymptotic stability of the steady motions in the unconstrained problem. Three effects caused by internal dissipation are established in a model example: stabilization of the satellites in a neighbourhood of rotations about a normal to the orbital plane, which is codirectional with the axis of the largest moment of inertia, evolution of elliptic orbits into circular orbits, and capture of the satellites in resonant oscillatory modes of motion. |
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