{"title":"On average values of nonlinear functions of oscillating quantities and their applications","authors":"Leonid Blekhman","doi":"10.35470/2226-4116-2023-12-2-103-110","DOIUrl":null,"url":null,"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.","PeriodicalId":37674,"journal":{"name":"Cybernetics and Physics","volume":"55 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cybernetics and Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35470/2226-4116-2023-12-2-103-110","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Physics and Astronomy","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
The scope of the journal includes: -Nonlinear dynamics and control -Complexity and self-organization -Control of oscillations -Control of chaos and bifurcations -Control in thermodynamics -Control of flows and turbulence -Information Physics -Cyber-physical systems -Modeling and identification of physical systems -Quantum information and control -Analysis and control of complex networks -Synchronization of systems and networks -Control of mechanical and micromechanical systems -Dynamics and control of plasma, beams, lasers, nanostructures -Applications of cybernetic methods in chemistry, biology, other natural sciences The papers in cybernetics with physical flavor as well as the papers in physics with cybernetic flavor are welcome. Cybernetics is assumed to include, in addition to control, such areas as estimation, filtering, optimization, identification, information theory, pattern recognition and other related areas.
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