振动量非线性函数的平均值及其应用

Q3 Physics and Astronomy

Cybernetics and Physics Pub Date : 2023-09-30 DOI:10.35470/2226-4116-2023-12-2-103-110

Leonid Blekhman

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引用次数: 0

摘要

非线性依赖关系中参数的振荡改变了各自函数的平均值。作为最简单的例子，球半径的谐波振荡增加了平均体积和表面积，而平均半径保持不变。尽管这些考虑是基本的，但往往被忽视，这可能导致不准确和错误。本文研究了这种效应在代数关系、几何关系和三角关系以及数学分析的某些基本公式中的应用。考虑了在解决技术问题方面的一些应用;特别是，参数振荡对工业操作效率的影响。研究结果可能对振动过程和装置理论、精度理论以及控制和优化过程理论感兴趣。

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

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.

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来源期刊

Cybernetics and Physics Chemical Engineering-Fluid Flow and Transfer Processes

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

10 weeks

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.