The semigroup approach to the problem of N bodies
Abstract
The semigroup approach to the problem of N bodies investigation is developed. The differential equation in partial differences for the problems, multitudes problem of N bodies with different initial conditions is shown. On the basis of the physical considerations, invariant transformations for radiusvectors are obtained which with the help of semigroup correlation make the problem of N bodies with special initial conditions possible. The differential equation for 3 bodies problem multitudes with different initial conditions is possible with the help of Ambartsumian's principle of invariance. The possibility of the common solving of this equation is discussed. The examples of the mechanical systems for which we manage to describe further evolution are shown.
 Publication:

Communications of the Byurakan Astrophysical Observatory
 Pub Date:
 1989
 Bibcode:
 1989CoBAO..61..124B
 Keywords:

 Classical Mechanics;
 Group Theory;
 Many Body Problem;
 Invariance;
 Partial Differential Equations;
 Three Body Problem;
 Transformations (Mathematics);
 Physics (General)