History of Krylov-Bogoliubov-Mitropolsky Methods of Nonlinear Oscillations - Advances in Historical Studies

AHS > Vol.6 No.1, March 2017

Advances in Historical Studies

Volume 6, Issue 1 (March 2017)

ISSN Print: 2327-0438 ISSN Online: 2327-0446

Google-based Impact Factor: 0.45 Citations

History of Krylov-Bogoliubov-Mitropolsky Methods of Nonlinear Oscillations ()

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DOI: 10.4236/ahs.2017.61003 2,315 Downloads 4,669 Views Citations

Author(s)

Agamenon R. E. Oliveira

Affiliation(s)

Polytechnic School of Rio de Janeiro, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil.

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.

KEYWORDS

Nonlinear Systems, Weakly Nonlinear Systems, Nonlinear Differential Equations, Perturbation Methods

Share and Cite:

Oliveira, A. (2017) History of Krylov-Bogoliubov-Mitropolsky Methods of Nonlinear Oscillations. Advances in Historical Studies, 6, 40-55. doi: 10.4236/ahs.2017.61003.

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