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About Direct Linearization Methods for Nonlinearity

  • Alishir A. AlifovEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1126)

Abstract

All real dynamic systems are nonlinear and potentially oscillatory, despite their separation into various types (physical, chemical, biological, economic, etc.). And the use of linear models that are valid only for small changes in parameters is associated with mathematical difficulties (finding solutions to nonlinear equations). Known methods of analysis and calculation of nonlinear systems have a significant drawback: high labor intensity and time - consuming. In contrast, direct linearization methods reduce these disadvantages by several orders of magnitude. Below are the methods of direct linearization for the calculation of nonlinear systems. Direct linearization of nonlinearity is considered in two cases. In the first case, the nonlinear function depends on one variable, and in the second - on two. Direct linearization methods are compared with a known averaging method. The procedure for applying direct linearization methods is described for calculating oscillatory systems interacting with energy sources.

Keywords

Method Nonlinearity Direct linearization Oscillations 

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Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Mechanical Engineering Research Institute of Russian Academy of SciencesMoscowRussia

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