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.
Grebenikov, Eugeniu; Mitropolsky, Yu. A.; Ryabov, Y.A.
"The book is well written and may be used by graduate students and researchers in both mechanics and applied mathematics." - Zentralblatt MATH, 1055 "This book should be very useful to scientists interested in efficient approximation methods for solutions of ordinary differential equations with good accuracy, with a substantial portion devoted to celestial mechanics. It should also be interesting to theorists and applied scientists, since it gives estimates on the proximity of solutions of non-integrable problems to solutions of averaged systems that my be fully integrated. .. [This book includes] examples of iterative processes and their convergence, especially useful for computer programming, either numerical or symbolic." - Mathematical Reviews, Issue 2005d
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