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Band 138

Stability of Motion

Aus der Reihe Grundlehren der mathematischen Wissenschaften

87,99 €

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

18.05.2012

Abbildungen

XII, 448 p. 35 illus.

Verlag

Springer Berlin

Seitenzahl

448

Maße (L/B/H)

23,5/15,5/2,5 cm

Gewicht

698 g

Auflage

Softcover reprint of the original 1st ed. 1967

Sprache

Englisch

ISBN

978-3-642-50087-9

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

18.05.2012

Abbildungen

XII, 448 p. 35 illus.

Verlag

Springer Berlin

Seitenzahl

448

Maße (L/B/H)

23,5/15,5/2,5 cm

Gewicht

698 g

Auflage

Softcover reprint of the original 1st ed. 1967

Sprache

Englisch

ISBN

978-3-642-50087-9

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: ProductSafety@springernature.com

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  • Produktbild: Stability of Motion
  • Produktbild: Stability of Motion
  • I. Generalities.- § 1. The Stability Concept in Mechanics.- § 2. Stability in the Sense of Liapunov.- II. Linear Functional Equations with Constant Coefficients.- § 3. Transfer Units.- § 4. Linear Differential Equations with Constant Coefficients.- § 5. Geometrical Criteria for Stability.- § 6. Algebraic Criteria for Stability.- § 7. Orlando’s Formula.- § 8. Linear Transfer Systems.- § 9. An Example.- § 10. The Nyquist Criterion.- § 11. The Boundary of Stability.- § 12. Linear Differential Difference Equations.- § 13. Stability for Linear Differential Difference Equations with Constant Coefficients.- § 14. Linear Difference Equations with Constant Coefficients.- § 15. Linear Operators.- III. The Equilibrium of Autonomous Differential Equations.- § 16. Fundamental Concepts, Definitions and Notations.- § 17. Homogeneous Right Side.- § 18. General Systems of the Second Order.- § 19. Second Order Systems with Homogeneous Right Sides.- § 20. Second Order Linear Systems.- § 21. Perturbed Second Order Linear Systems.- § 22. Conservative Second Order Systems.- IV. The Direct Method of Liapunov.- § 23. Geometric Interpretation.- § 24. Some Subsidiary Considerations.- § 25. The Principal Theorems of the Direct Method for Autonomous Differential Equations.- § 26. Supplements to the Principal Theorems.- § 27. Construction of a Liapunov Function for a Linear Equation.- § 28. Liapunov Functions for Perturbed Linear Equations.- § 29. The Problem of Aizerman.- § 30. Further Applications of the Direct Method.- § 31. Absolute Stability.- § 32. Popov’s Criterion.- § 33. The Domain of Attraction.- § 34. Zubov’s Theorem.- V. The Direct Method for General Motions.- § 35. The General Stability Concept.- § 36. Extensions and Modifications of the BasicDefinitions.- § 37. Instability and Non-Uniform Stability.- § 38. Relationships between the Stability Types.- § 39. Realizing Some Stability Types.- § 40. An Example for Instability.- § 41. Liapunov Functions.- § 42. Tests for Stability.- § 43. Applications and Examples. I. Differential and Difference Equations.- § 44. Applications and Examples. II. Functional and Partial Differential Equations.- § 45. System Stability and Stability of Invariant Sets.- § 46. Boundedness Criteria. The Parallel Theorems.- VI. The Converse of the Stability Theorems.- § 47. Formulation of the Problem.- § 48. The Converse of the Theorems on Non-Asymptotic Stability.- § 49. The Converse of Theorems on Asymptotic Stability.- § 50. Examples for the Converse Theorems.- § 51. Refinements of the Converse Theorems for Ordinary Differential Equations.- § 52. The Converse of the Instability Theorems.- VII. Stability Properties of Ordinary Differential Equations.- § 53. The Meaning of the Decrescence of Liapunov Functions.- § 54. Existence of a Liapunov Function in Case of Non-Uniform Asymptotic Stability.- § 55. Modified Stability Criteria.- § 56. Perturbed Equations.- § 57. Equations with Homogeneous Right Side.- VIII. Linear Differential Equations.- § 58. The General Solution of a Linear Homogeneous Differential Equation.- § 59. The Nonhomogeneous Linear Equation.- § 60. Linear Equations with Periodic Coefficients.- § 61. The Liapunov Reducibility Theorem.- § 62. Stability Criteria for Special Linear Differential Equations.- § 63. The Order Numbers of a Differential Equation.- § 64. Regular Differential Equations.- § 65. Stability in the First Approximation.- IX. The Liapunov Expansion Theorem.- § 66. Families of Solutions Depending on a Parameter.- § 67. TheLiapunov Expansion Theorem.- X. The Critical Cases for Differential Equations.- § 68. General Remarks Concerning Critical Cases; Subsidiary Results.- § 69. The Principal Theorem of Malkin.- § 70. Simple Critical Cases for Autonomous Equations.- XI. Periodic and Almost Periodic Motions.- § 71. General Remarks on periodic Motions.- § 72. Nonhomogeneous Linear Equations with Periodic External Force.- § 73. Forced Almost Periodic Oscillations.- § 74. Piecewise Linear Equations.- § 75. A System with Several Discontinuity Types.- § 76. Perturbed Linear Equations.- § 77. Perturbed Linear Equations for the Resonance Case.- § 78. Periodic Solutions of Autonomous Equations.- § 79. Critical Cases of Second Order Autonomous Systems.- § 80. The Associated Coordinate System of a Periodic Solution.- § 81. Stability Properties of a Periodic Solution.- § 82. Examples: Testing for Stability.- Author Index.