G. A. Leonov, I. M. Burkin, A. I. Shepeljavyi

Frequency Methods in Oscillation Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

Zur Zeit liegt uns keine Inhaltsangabe vor.

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Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 404
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9789400901933
• Artikelnr.: 43982170

Inhaltsangabe

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.