On average values of nonlinear functions of oscillating quantities and their applications

Abstract

Oscillations of arguments in non-linear dependencies change the average values of respective functions. As the simplest example, the harmonic oscillations of the ball radius increase the average volume and surface area, while the average radius remains unchanged. Despite their elementary nature, such considerations are often ignored, which may lead to inaccuracies and errors. This paper presents a study of such effects in algebraic, geometric and trigonometric relations, as well as in certain basic formulas of mathematical analysis. A number of applications in solving technical problems are considered; in particular, the influence of parameter oscillations on the efficiency of industrial operations. The results of the study may be of interest for the theory of vibrational processes and devices, and the theory of accuracy, as well as for the theory of control and optimal processes.