By Vladimir Nikolov Damgov
The ebook includes a huge landscape of phenomena happening in 4 significant periods of radiophysical and mechanical structures -- linear, nonlinear, parametric, and nonlinear-parametric. An analytical process for the huge circle of concerns into account is built. it truly is offered in a undemanding shape, permitting its additional direct software in examine practices. Analytical equipment are provided for investigating modulation-parametric and nonlinear structures, oscillating platforms with periodic and virtually periodic time-dependent parameters, results of adaptive self-organization in coupled resonance platforms and oscillating platforms below the motion of exterior forces, nonlinear with appreciate to the coordinates of excited structures. Of an interdisciplinary nature, this quantity can function a guide for constructing lecture classes similar to basics of Nonlinear Dynamics and conception of Nonlinear Oscillations, concept of Nonlinear Circuits and structures, basics of Radiophysics and Electronics, concept of signs and Theoretical Radiophysics, Theoretical Mechanics and Electrodynamics.
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Additional resources for Nonlinear And Parametric Phenomena: Theory And Applications In Radiophysical And Mechanical Systems (World Scientific Series on Nonlinear Science, Series a)
21) to obtain 00 l^ 00 00 l^ . . 22). As we generalize that for the case of an explicitly time-dependent and periodic nonlinear capacitance and two exciting generators, the following energy relations are obtained: oo oo OO 2^ OO oo ... OO T T^ 2^ 2L, nfl + n2f2 + nf ~ U> ni = - o o n 2 = 0 n = - o o oo oo oo Z^ JX (L23) J „ . 23) can be generalized for the case of k generators by using the method of mathematical induction. ,nk,n 2-ii=l niJi E n i ,... ,ii t ,71 „ m nk,nT,*=inifi+nf For the purpose of simplifying the written form, we have introduced an abbreviated denotation of the multiple sums, given that all variables subject to summation fall in the range from —oo to +oo, except for the underlined variable, whose range is from 0 to oo.
Papaleksi [44-53, 118]. The works of the classics listed above lay out the foundations of the theory of periodic motions, of ponderomotive interactions of different oscillating systems. A. Einstein made wide use of oscillating analogues to describe the heat-consuming property and solidity of substances. It is worth noting that in spite of the availability of a number of wonderful models (those of Gins, Tyuring, Eigen, Zhabotinski-Belousov and many more), the modern stage in the development of synergetics as a scientific area is related to the analysis of most simple basic models, which serve as a foundation for exploring some general features of the processes of adaptive grouping and self-organization.
Into Mathieu's and Hill's equations. In fact these are equations with constant coefficients and a specific nonlinear right-hand part. Given a non-zero amplitude A of the argument external force, over a certain part of the period — the argument of the shift along the coordinate will run ahead of the argument of acceleration, while during the remaining part of the period it will lag behind that argument. ), which may lead to the excitation of continuous oscillations. The foundation for studying these processes is the analysis, from the general positions of the Theory of nonlinear oscillations, of the processes and phenomena well-known in Radiophysics, Electromechanics, Microwave electronics, Optics, technology for accelerating charged particles, etc.
Nonlinear And Parametric Phenomena: Theory And Applications In Radiophysical And Mechanical Systems (World Scientific Series on Nonlinear Science, Series a) by Vladimir Nikolov Damgov