Year: 1915
Type: article
Abstract: The known isosceles-triangle solutions of the problem of three bodies are the periodic solutions in which two of the bodies have equal finite masses, while the third body moves in a straight line and remains equidistant from the other bodies. In my Chicago dissertationt three cases of the isoscelestriangle solutions were discussed. In the first case the finite bodies move in a circle and the third body is infinitesimal. The solution of this case was first obtained by Pavaninit by means of elliptic integrals, and was later developed independently by MacMillan.? The solution which was obtained in my dissertation is analogous to that obtained by MacMillan. In the second case, not treated by Pavanini and MacMillan, the finite bodies move in ellipses and the third body is infinitesimal. In the third case, all three bodies are finite. The period of the motion in case III is the same as that in case I, and the solution reduces to the solution of the first case when the third body becomes infinitesimal. The present paper is an extension of the second case of my dissertation to that in which all three masses are finite. Periodic orbits are here shown to exist, and a practical method is given of computing them. These solutions have the same period as those of case II of my dissertation, and reduce to them when the third body becomes infinitesimal.
Author: Daniel Buchanan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2069604460