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Equilibria in the gravitational field of a triangular body. (English) Zbl 1448.70034
Summary: 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.
70F15 Celestial mechanics
70F07 Three-body problems
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