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Non-linear dynamics of ring world systems

McInnes, C.R. (2003) Non-linear dynamics of ring world systems. JBIS, Journal of the British Interplanetary Society, 56 (9-10). pp. 308-313. ISSN 0007-084X

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The dynamics of a point mass and a thin solid ring are considered with the point mass located within the perimeter of the ring. It is demonstrated that an equilibrium configuration exists only when the center-of-mass of the ring and the point mass are collocated. However, this sole equilibrium configuration is unstable due to perturbations within the plane of the ring, but is stable due to perturbations normal to the plane of the ring. Such a ring system about a star has been envisaged in some detail in well-known works of fiction. While qualitative, or sometimes quantitative linear analysis of the problem is to be found, a full non-linear analysis of the dynamics of the problem does not appear to have been previously published.