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New coordinates for three‐body problems
Author(s) -
Bleick W. E.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560220825
Subject(s) - bipolar coordinates , log polar coordinates , action angle coordinates , orthogonal coordinates , generalized coordinates , prolate spheroidal coordinates , coordinate system , parabolic coordinates , physics , cylindrical coordinate system , curvilinear coordinates , classical mechanics , rotation (mathematics) , cartesian coordinate system , point (geometry) , plane (geometry) , spherical coordinate system , ellipsoidal coordinates , normal coordinates , planar , geometry , mathematics , computer science , mechanics , quantum mechanics , computer graphics (images) , molecule
A symmetrical system of coordinates is proposed for studying the planar motion of a three‐body system of point masses in its internal degrees of freedom. The three coordinate axes pass through the masses, with the positive halves intersecting at angles of 120° to each other at a moving origin. The coordinates are taken as the signed distances of the masses from the moving origin, and the angle of rotation of the coordinate axes in the plane. The transformation from the intermass distances to the coordinates is found. The small vibrations of the masses when interconnected by springs is studied as an application of the new coordinates. Some remarks are made about the stability of the numerical solution of the gravitational three‐body problem, and about the asymptotic form of the potential for large and positive values of the coordinates.