The Two-Center Problem on a Sphere
The problem of two fixed centers consists in determining the motion of a material point which is attracted by two fixed point masses according to the Newton law. It was Euler, who first considered the two-center problem and reduced it to quadratures. He showed the integrability of this problem and studied the simplest motions (1760). The classification of the motion for the plane case was carried out by Charlier  (1907). However his analysis turned out to be incomplete and partially incorrect, so it has been corrected twice by Tallqvist  (1927) and Badalyan . In the paper of Alekseev  the generalized three-dimensional problem of the two-center problem was studied, the qualitative analysis and the classification of motions were carried out.
KeywordsBifurcation Diagram Configuration Space Bifurcation Curve Kepler Problem Critical Circle
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