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Titlebook: Oscillators and Oscillatory Signals from Smooth to Discontinuous; Geometrical, Algebra Valery N. Pilipchuk Book 2023Latest edition Springer

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发表于 2025-3-21 18:46:48 | 显示全部楼层 |阅读模式
书目名称Oscillators and Oscillatory Signals from Smooth to Discontinuous
副标题Geometrical, Algebra
编辑Valery N. Pilipchuk
视频video
概述Presents an improved picture of non-smooth temporal transformations using impact systems as a basis for various analyses.Includes new examples of recent applications for problems in energy absorption/
图书封面Titlebook: Oscillators and Oscillatory Signals from Smooth to Discontinuous; Geometrical, Algebra Valery N. Pilipchuk Book 2023Latest edition Springer
描述This updated and enriched new edition maintains its complementarity principle in which the subgroup of rotations, harmonic oscillators, and the conventional complex analysis generate linear and weakly nonlinear approaches, whereas translations and reflections, impact oscillators, and hyperbolic Clifford’s algebras, give rise to the essentially nonlinear “quasi-impact” methodology based on the idea of non-smooth temporal substitutions. In the years since “Nonlinear Dynamics: Between Linear and Impact Limits,” the previous edition of this book, was published, due to a widening area of applications, a deeper insight into the matter has emerged leading to the rudimentary algebraic view on the very existence of the complementary smooth and non-smooth base systems as those associated with two different signs of the algebraic equation .j2 =± 1.. This edition further includes an overview of applications found in the literature after the publication of first edition, and new physical examples illustrating both theoretical statements and constructive analytical tools.. .
出版日期Book 2023Latest edition
关键词NSTT; Non-Smooth Processes; Non-Smooth Temporal Transformations; Nonlinear Dynamics; Nonlinear Processes
版次2
doihttps://doi.org/10.1007/978-3-031-37788-4
isbn_softcover978-3-031-37790-7
isbn_ebook978-3-031-37788-4
copyrightSpringer Nature Switzerland AG 2023
The information of publication is updating

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Strongly Nonlinear Waves,unctions of the triangle wave based on the algorithms of the previous chapter. Then the differential equations for slow varying modulations are derived by using the Whitham assumptions and the specific boundary conditions associated with nonsmooth argument substitutions.
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Singular Trajectories of Forced Vibrations,ion is still possible in terms of eigenvector-functions of time given by NSTT boundary value problems. Physical meaning of the corresponding nonlinear definitions for both discrete and continual models is discussed.
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Book 2023Latest editiontional complex analysis generate linear and weakly nonlinear approaches, whereas translations and reflections, impact oscillators, and hyperbolic Clifford’s algebras, give rise to the essentially nonlinear “quasi-impact” methodology based on the idea of non-smooth temporal substitutions. In the year
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Smooth Oscillating Processes,minary transformation of the original system to the form that admits a straightforward solution. In particular, the averaging algorithm based on the Hausdorff equation for operators Lie is reproduced.
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Strongly Nonlinear Vibrations,stems are described in the next three sections. Then the description focuses on the algorithm implementations for different essentially anharmonic cases including oscillators whose characteristics may approach nonsmooth or even discontinuous limits.
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