About Direct Linearization Methods for Nonlinearity

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.