Frequency Methods in Oscillation Theory

Lingua: inglese

Editore: Springer, Springer Dez 1995, 1995

0792338960 / 9780792338963

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This item is printed on demand - Print on Demand Titel. Neuware -1. Classical two-dimensional oscillating systems and their multidimensional analogues.- 1.1. The van der Pol equation.- 1.2. The equation of oscillations of a pendulum.- 1.3. Oscillations in two-dimensional systems with hysteresis.- 1.4. Lower estimates of the number of cycles of a two-dimensional system.- 2. Frequency criteria for stability and properties of solutions of special matrix inequalities.- 2.1. Frequency criteria for stability and dichotomy.- 2.2. Theorems on solvability and properties of special matrix inequalities.- 3. Multidimensional analogues of the van der Pol equation.- 3.1. Dissipative systems. Frequency criteria for dissipativity.- 3.2. Second-order systems. Frequency realization of the annulus principle.- 3.3. Third-order systems. The torus principle.- 3.4. The main ideas of applying frequency methods for multidimensional systems.- 3.5. The criterion for the existence of a periodic solution in a system with tachometric feedback.- 3.6. The method of transition into the 'space of derivatives'.- 3.7. A positively invariant torus and the function 'quadratic form plus integral of nonlinearity'.- 3.8. The generalized Poincaré-Bendixson principle.- 3.9. A frequency realization of the generalized Poincaré-Bendixson principle.- 3.10. Frequency estimates of the period of a cycle.- 4. Yakubovich auto-oscillation.- 4.1. Frequency criteria for oscillation of systems with one differentiable nonlinearity.- 4.2. Examples of oscillatory systems.- 5. Cycles in systems with cylindrical phase space.- 5.1. The simplest case of application of the nonlocal reduction method for the equation of a synchronous machine.- 5.2. Circular motions and cycles of the second kind in systems with one nonlinearity.- 5.3. The method ofsystems of comparison.- 5.4. Examples.- 5.5. Frequency criteria for the existence of cycles of the second kind in systems with several nonlinearities.- 5.6. Estimation of the period of cycles of the second kind.- 6. The Barbashin-Ezeilo problem.- 6.1. The existence of cycles of the second kind.- 6.2. Bakaev stability. The method of invariant conical grids.- 6.3. The existence of cycles of the first kind in phase systems.- 6.4. A criterion for the existence of nontrivial periodic solutions of a third-order nonlinear system.- 7. Oscillations in systems satisfying generalized Routh-Hurwitz conditions. Aizerman conjecture.- 7.1. The existence of periodic solutions of systems with nonlinearity from a Hurwitzian sector.- 7.2. Necessary conditions for global stability in the critical case of two zero roots.- 7.3. Lemmas on estimates of solutions in the critical case of one zero root.- 7.4. Necessary conditions for absolute stability of nonautonomous systems.- 7.5. The existence of oscillatory and periodic solutions of systems with hysteretic nonlinearities.- 8. Frequency estimates of the Hausdorff dimension of attractors and orbital stability of cycles.- 8.1. Upper estimates of the Hausdorff measure of compact sets under differentiable mappings.- 8.2. Estimate of the Hausdorff dimension of attractors of systems of differential equations.- 8.3. Global asymptotic stability of autonomous systems.- 8.4. Zhukovsky stability of trajectories.- 8.5. A frequency criterion for Poincaré stability of cycles of the second kind.- 8.6. Frequency estimates for the Hausdorff dimension and conditions for global asymptotic stability.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 420 pp. Englisch.

Codice articolo 9780792338963

Titolo
Frequency Methods in Oscillation Theory
Autore
G. A. Leonov
Editore
Springer, Springer Dez 1995
Anno di pubblicazione
1995
Condizione
Neu
Rilegatura
Buch
Lingua
inglese
ISBN 10
0792338960
ISBN 13
9780792338963
Peso dell'articolo
793 grammi
Dimensioni
241x160x28 mm

buchversandmimpf2000

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