Knowing minimum to understand maximum. The realm of nonlinear oscillations is enormous. The book introduces possibly the most compact, simple and physically understandable apparatus that can describe, explain, predict and design the widest set of phenomena in time variant and nonlinear oscillations: parametric resonances, combined resonances, instability of forced oscillations, synchronization, distributed parameter oscillation and flatter, parametric oscillation control, robustness of oscillations and many others.
This unique tool is the method of stationarization or one frequency approximation of parametric resonance problem analysis in linear time variant dynamic systems. It is shown how it can explain periodic motion stability in stationary nonlinear dynamic systems. The book reveals the link between the harmonic stationarization coefficients and describing functions. Thus, the books speaks the language of control: transfer functions, frequency response, Nyquist plot, stability margins etc.
The understanding of physics of stability loss lays the ground to the design of new methods to oscillation control, several new methods are presented in the book. These and all the other findings are illustrated by numerical examples, that can be easily reproduced by the reader equipped with basic simulation package like Matlab with Simulink. The book is intendent for all travelling through the world of oscillations. Students can find a simple tool to navigate through and to witness the hidden beauty of this world. Researchers can use the method for conquering its unknown parts as well as a reference to compare with what they have been doing by other, for example, abstract mathematical means. Engineers can finally find a minimalistic but powerful applicable instrument based on physically measurable variables to analyze and design oscillatory systems. And for all cases, he hope, knowing minimum to understand maximum.
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