Book Review: Forced oscillations in non-linear systems
نویسندگان
چکیده
منابع مشابه
Forced Oscillations in a Linear System
Annotation. The manual includes a description of the simulated physical system and a summary of the relevant theoretical material for students as a prerequisite for the virtual lab “Forced Oscillations of Linear Torsion Pendulum.” The manual includes also a set of theoretical and experimental problems to be solved by students on their own, as well as various assignments which the instructor can...
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The use of delayed feedback of position for the control of oscillatory behaviour is analysed. It is shown that linear feedback can annihilate limit cycles and stabilize the origin. Furthermore, it is possible to create an asymptotically stable limit cycle with any prescribed amplitude using a simple nonlinear feedback. For almost all values of the delay, these feats can be achieved without usin...
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The definition of a non-linear normal mode (NNM) as an invariant manifold in phase space is used. In conservative cases, it is shown that normal form theory allows one to compute all NNMs, as well as the attendant dynamics onto the manifolds, in a single operation. Then, a single-mode motion is studied. The aim of the present work is to show that too severe trunc ature using a single linear mod...
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The principal features of two mathematical models that can be used to study non-linear oscillations of a workpiece – tool system during a milling operation are presented and explained in this article. These models are non-linear, non-homogeneous, delay-differential systems with time-periodic coefficients. In the treatment presented here, the sources of non-linearities are the multiple regenerat...
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Formation of spatially localized oscillations in parametrically driven systems is studied, focusing on the dominant 2:1 resonance tongue. Both damped and self-excited oscillatory media are considered. Near the primary subharmonic instability such systems are described by the forced complex Ginzburg–Landau equation. The technique of spatial dynamics is used to identify three basic types of coher...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1954
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1954-09865-8