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Equilibria in the gravitational field of a triangular body

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Abstract

The existence, stability and bifurcation analysis is performed for equilibria of a material point in the gravitational field of three homogeneous penetrable balls fixed in absolute frame. The radii of the balls are assumed finite. In the case when the mass distribution admits a symmetry axis, analytic expressions are written out, allowing one to investigate the properties of equilibrium positions located both on the symmetry axis and outside it. The stability of solutions is studied; domains with different instability degree are described.

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Correspondence to Anna D. Guerman.

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This research is partially supported by RFBR, Grants 16-01-00625 and 18-01-00335, project EMaDeS (Centro-01-0145-FEDER-000017), and the Portuguese Foundation for Science and Technologies via Centre for Mechanical and Aerospace Science and Technologies, C-MAST, POCI-01-0145-FEDER-007718. V. I. Nikonov: On leave from FRC “Computer Science and Control” of the Russian Academy of Science.

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Burov, A.A., Guerman, A.D. & Nikonov, V.I. Equilibria in the gravitational field of a triangular body. Celest Mech Dyn Astr 130, 58 (2018). https://doi.org/10.1007/s10569-018-9850-8

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  • DOI: https://doi.org/10.1007/s10569-018-9850-8

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