Methods of Accelerated Convergence in Nonlinear Mechanics by V. Kumar Paperback | Indigo Chapters - neues Buch

EAN (ISBN-13): 9783642619021
ISBN (ISBN-10): 3642619029
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2011
Herausgeber: Springer Berlin

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ISBN/EAN: 9783642619021

ISBN - alternative Schreibweisen:
3-642-61902-9, 978-3-642-61902-1
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: sneddon, bogoljubov, kumar, kolmogorov
Titel des Buches: methods accelerated convergence nonlinear mechanics, accelerate

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Daten vom Verlag:

Autor/in: N.N. Bogoljubov; J.A. Mitropoliskii; A.M. Samoilenko
Titel: Methods of Accelerated Convergence in Nonlinear Mechanics
Verlag: Springer; Springer Berlin
291 Seiten
Erscheinungsjahr: 2011-11-15
Berlin; Heidelberg; DE
Gedruckt / Hergestellt in Niederlande.
Übersetzer/in: V. Kumar
Gewicht: 0,522 kg
Sprache: Englisch
53,49 € (DE)
54,99 € (AT)
59,00 CHF (CH)
POD
VIII, 291 p.

BC; Engineering, general; Hardcover, Softcover / Technik; Ingenieurswesen, Maschinenbau allgemein; Verstehen; Convergence; Technology and Engineering; BB

0. Introduction.- 1. Quasi-Periodic Solutions in Problems of Nonlinear Mechanics.- § 1. Statement of the Problem. The Existence of an Invariant Manifold.- § 2. Auxiliary Theorems.- § 3. Lemma on Iterations.- § 4. Theorem on Quasi-Periodic Solutions.- § 5. Parametric Dependence of Quasi-Periodic Solutions. Asymptotic and Convergent Expansions.- § 6. Quasi-Periodic Solutions in Second Order Systems.- 2. General Solutions of Nonlinear Differential Equations in the Neighbourhood of Quasi-Periodic Solutions.- § 7. Statement of the Problem.- § 8. Some Auxiliary Statements.- § 9. Inductive Theorem.- § 10. Iteration Process and its Convergence.- § 11. Theorem on Reducibility of Nonlinear Equations.- 3. A Smoothing Technique.- § 12. Loss of Derivatives.- § 13. Examples of Smoothing Operators.- § 14. The Basic Properties of a Smoothing Operator.- § 15. Iteration Process with Smoothing.- 4. Trajectories on a Torus.- § 16. Behaviour of Trajectories on a Two-Dimensional Torus.- § 17. Behaviour of Trajectories on an m-Dimensional Torus.- § 18. Inductive Theorem.- § 19. Proof of the Theorem on the Reducibility of Equations on a Torus.- 5. Linear Systems with Quasi-Periodic Coefficients.- § 20. Reducibility Theorem.- § 21. Solution of the Auxiliary Equation.- § 22. Proof of Reducibility Theorem.- § 23. Construction of a Fundamental Matrix of Solutions.- § 24. The Measure of Reducible Systems. Statement of the Problem.- § 25. A Generalized Reducibility Theorem.- § 26. Metric Propositions.- § 27. Proof of the Measure Theorem.- § 28. Linear Systems with Smooth Right-Hand Sides.- 6. Neighbourhood of an Invariant Smooth Toroidal Manifold.- § 29. Behaviour of Integral Curves in the Neighbourhood of Toroidal Manifolds.- § 30. Auxiliary Propositions.- § 31. Iteration Theorem.- § 32. Reducibility Theorem in the Neighbourhood of a Toroidal Manifold.- § 33. Behaviour under Perturbation of Integral Curves in the Neighbourhood of an Invariant Manifold.- 7. Neighbourhood of a Compact Invariant Manifold of a Non-Autonomous System.- § 34. Statement of the Problem and Basic Postulates.- § 35. Lemma on the Solutions of an Auxiliary System.- § 36. Inductive Theorem.- § 37. Neighbourhood of an Invariant Manifold.- § 38. Behaviour of Solutions of a System of Two Equations in the Neighbourhood of Equilibrium Positions.- Appendices I to XV.- References.