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History of Krylov-Bogoliubov-Mitropolsky Methods of Nonlinear Oscillations
Polytechnic School of Rio de Janeiro, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil
- 1 Polytechnic School of Rio de Janeiro, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil
Advances in Historical Studies·Volume 06 (2017)·Pages 40–55·Published 21 March 2017·DOI10.4236/ahs.2017.61003
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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.
KeywordsNonlinear SystemsWeakly Nonlinear SystemsNonlinear Differential EquationsPerturbation Methods
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