Institute for High-Performance Computer Systems RAS, Moscow
In E. A. Grebenikov and U. A. Rybov monograph " The new qualitative methods of celestial mechanics " ( Edition "Nauka", 1971 ) is shown, that assymptotical solution of the Cauchy differential equations problem of the celestial mechanics contains "secular" function, if the high degree iterations are constructed with the zero initial conditions. At the expense of change of the initial conditions it is possible to destroy the "secular" terms in assymptotical formulas, which present the solution. The new initial conditions are defined as a result of the solution of the some transcendental functional equation system by a method of simple iterations. Hansen has offered to destroy the "secular" terms in perturbation theory of planetary movements by the introduction, so named, " average elements ", but has not given this mathematical substantation. The appropriate programs are designed.