Krylov–Bogoliubov averaging method

The Krylov–Bogolyubov averaging method (Krylov–Bogolyubov method of averaging) is a mathematical method for approximate analysis of oscillating processes in non-linear mechanics. The method is based on the averaging principle when the exact differential equation of the motion is replaced by its averaged version. The method is named after Nikolay Krylov and Nikolay Bogoliubov.

Various averaging schemes for studying problems of celestial mechanics were used since works of Carl Friederich Gauss, Pierre Fatou, Boris Delone and George William Hill. The importance of the contribution of Krylov and Bogoliubov is that they developed a general averaging approach and proved that the solution of the averaged system approximates the exact dynamics.

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