Asymptotic Methods in Resonance Analytical Dynamics

ISBN-13: 9780415310086 / Angielski / Twarda / 2004 / 278 str.

E. A. Grebenikov; Eugeniu Grebenikov; Yu A. Mitropolsky

Opis

Asymptotic Methods in Resonance Analytical Dynamics presents new asymptotic methods for the analysis and construction of solutions (mainly periodic and quasiperiodic) of differential equations with small parameters. Along with some background material and theory behind these methods, the authors also consider a variety of problems and applications in nonlinear mechanics and oscillation theory. The methods examined are based on two types: the generalized averaging technique of Krylov-Bogolubov and the numeric-analytical iterations of Lyapunov-Poincare. This text provides a useful source of reference for postgraduates and researchers working in this area of applied mathematics."

Spis treści

Asymptotic Methods in Resonance Analytical Dynamics presents new techniques for the analysis and construction of solutions to nonlinear, multi-frequency differential equations with small parameters. The authors examine two types of methods: Methods based on the generalized averaging technique of Krylov--Bogolubov, particularly useful in resonance cases, and methods based on numeric-analytic iterations, which can be automated. Along with some background material and theory behind these methods, the authors also consider a variety of problems and applications in nonlinear mechanics and oscillation theory, such as the Newtonian three-body problem and the motion of a geostationary satellite.

O autorze

Grebenikov, Eugeniu; Mitropolsky, Yu. A.; Ryabov, Y.A.