Dynamics of multibody chains in circular orbit: non-integrability of equations of motion |
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Authors: | Andrzej J Maciejewski Maria Przybylska |
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Institution: | 1.Janusz Gill Institute of Astronomy,University of Zielona Góra,Zielona Góra,Poland;2.Institute of Physics,University of Zielona Góra,Zielona Góra,Poland |
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Abstract: | This paper discusses the dynamics of systems of point masses joined by massless rigid rods in the field of a potential force. The general form of equations of motion for such systems is obtained. The dynamics of a linear chain of mass points moving around a central body in an orbit is analysed. The non-integrability of the chain of three masses moving in a circular Kepler orbit around a central body is proven. This was achieved thanks to an analysis of variational equations along two particular solutions and an investigation of their differential Galois groups. |
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