A transformation, which is a generalization of the Nekhyil transformation for the limited three-body problem is considered for the equations of the many-body problem in a moveable system of coordinates. The angle of natural rotation of the movable system of coordinates is taken as the independent variable, while the coordinates are subjected to a compression transformation. It is shown that the equations of motion after this transformation preserve the symmetry properties of the solutions, known for the initial equations.
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