History of Krylov-Bogoliubov-Mitropolsky Methods of Nonlinear Oscillations

Abstract

This paper presents and discusses the mathematical developments of the so-called Krylov-Bogoliubov-Mitropolsky (KBM) contribution to nonlinear dynamics. A brief biography of their common academic work at Kiev University, initially by Krylov and Bogoliubov and afterwards by Bogoliubov and Mitropolsky, is presented. The first book published by Krylov and Bogoliubov, Introduction to Nonlinear Mechanics, is analyzed showing their technological concerns. A selection of their works and books is also looked at and discussed.