Abstract
The present article gives a historical survery of G.D. Birkhoff's seventh problem which is an inquiry about the topological structure of the set of definition of the reduced differential equations of motion. Recent advances in the problem and their meaning have been briefly indicated.
The classical 3-body problem concerns how the three particles should move under their mutual Newtonian attraction. By a particle we mean a goometrical point endorsed with a constant positive numberm which is called mass. Expressed mathematically, the problem appears as to solving of the following system of differential equations:
wherex i,y i,z i signify the rectangular coordinates of thei-th particle andr ij denotes the distance between thei -th and the j-th particle. There are ten algebraic integrals of the system (1) describing the motion of the centre of gravity of the particles togather with conservation of angular momentum and conservation of energy.
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Chin-Chu, T. A brief account of G.D. Birkhoff's problem in the problem of three bodies. Appl Math Mech 1, 225–230 (1980). https://doi.org/10.1007/BF01876746
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DOI: https://doi.org/10.1007/BF01876746