Comment on ‘Stability and chaos of a damped satellite partially filled with liquid’ [Acta Astronautica 65 (2009) 1628–1638] |
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| Institution: | 1. Departamento de Matemáticas, Fac. Ciencias Experimentales, University of Huelva, Avda. Tres de Marzo s/n, 21071 Huelva, Spain;2. Departamento de Matemática Aplicada II, E.S. Ingenieros, University of Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain;1. Department of Aerospace Engineering, Tokyo Metropolitan University, 6-6 Asahigaoka, Hino, Tokyo 191-0065, Japan;2. School of Aerospace, Mechanical, and Manufacturing Engineering, Royal Melbourne Institute of Technology, Melbourne, VIC 3083, Australia;1. Institute of Technical Mechanics NASU & SSAU, Dnipro, Ukraine;2. Technical University of Madrid, Madrid, Spain;1. School of Astronautics, Northwestern Polytechnical University, Xi''an, 710072, PR China;2. National Key Laboratory of Aerospace Flight Dynamics, Northwestern Polytechnical University, Xi''an, 710072, PR China;3. Department of Mechanical Engineering, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada |
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| Abstract: | In the commented paper the authors consider a model for a damped satellite partially filled with liquid. They claim to prove the existence of Sil'nikov homoclinic and heteroclinic orbits using the undetermined coefficient method. It is enough to read their Theorem 3 to understand that their results are incorrect: according to it, if the equilibria are saddle-foci the existence of Sil'nikov homoclinic and heteroclinic connections is guaranteed. As we show along this comment, their conclusions are erroneous because the form of the function they assume for the global connections is incongruous. |
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