Introduction to the Theory of Stability

AvDavid R. Merkin,F.F. Afagh

Häftad, Engelska, 2011

Del 24 i serien Texts in Applied Mathematics

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Beskrivning

Many books on stability theory of motion have been published in various lan guages, including English. Also, using appropriate examples, he demonstrates the process of investigating the stability of motion from the formulation of a problem and obtaining the differential equations of perturbed motion to complete analysis and recommendations.

Produktinformation

Utgivningsdatum:2011-09-17
Mått:155 x 235 x 19 mm
Vikt:522 g
Format:Häftad
Språk:Engelska
Serie:Texts in Applied Mathematics
Antal sidor:320
Upplaga:1997
Förlag:Springer-Verlag New York Inc.
ISBN:9781461284772
Översättare:F.F. Afagh, A.L. Smirnov, F. F. Afagh, A. L. Smirnov

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Innehållsförteckning

1 Formulation of the Problem.- 1.1 Basic Definitions.- 1.2 Equations of Perturbed Motion.- 1.3 Examples of Derivation of Equations of a Perturbed Motion.- 1.4 Problems.- 2 The Direct Liapunov Method. Autonomous Systems.- 2.1 Liapunov Functions. Sylvester’s Criterion.- 2.2 Liapunov’s Theorem of Motion Stability.- 2.3 Theorems of Asymptotic Stability.- 2.4 Motion Instability Theorems.- 2.5 Methods of Obtaining Liapunov Functions.- 2.6 Application of Liapunov’s Theorem.- 2.7 Application of Stability Theorems.- 2.8 Problems.- 3 Stability of Equilibrium States and Stationary Motions of Conservative Systems.- 3.1 Lagrange’s Theorem.- 3.2 Invertibility of Lagrange’s Theorem.- 3.3 Cyclic Coordinates. The Routh Transform.- 3.4 Stationary Motion and Its Stability Conditions.- 3.5 Examples.- 3.6 Problems.- 4 Stability in First Approximation.- 4.1 Formulation of the Problem.- 4.2 Preliminary Remarks.- 4.3 Main Theorems of Stability in First Approximation.- 4.4 Hurwitz’s Criterion.- 4.5 Examples.-4.6 Problems.- 5 Stability of Linear Autonomous Systems.- 5.1 Introduction.- 5.2 Matrices and Basic Matrix Operations.- 5.3 Elementary Divisors.- 5.4 Autonomous Linear Systems.- 5.5 Problems.- 6 The Effect of Force Type on Stability of Motion.- 6.1 Introduction.- 6.2 Classification of Forces.- 6.3 Formulation of the Problem.- 6.4 The Stability Coefficients.- 6.5 The Effect of Gyroscopic and Dissipative Forces.- 6.6 Application of the Thomson-Tait-Chetaev Theorems.- 6.7 Stability Under Gyroscopic and Dissipative Forces.- 6.8 The Effect of Nonconservative Positional Forces.- 6.9 Stability in Systems with Nonconservative Forces.- 6.10 Problems.- 7 The Stability of Nonautonomous Systems.- 7.1 Liapunov Functions and Sylvester Criterion.- 7.2 The Main Theorems of the Direct Method.- 7.3 Examples of Constructing Liapunov Functions.- 7.4 System with Nonlinear Stiffness.- 7.5 Systems with Periodic Coefficients.- 7.6 Stability of Solutions of Mathieu-Hill Equations.- 7.7 Examples of Stability Analysis.- 7.8 Problems.- 8 Application of the Direct Method of Liapunov to the Investigation of Automatic Control Systems.- 8.1 Introduction.- 8.2 Differential Equations of Perturbed Motion of Automatic Control Systems.- 8.3 Canonical Equations of Perturbed Motion of Control Systems.- 8.4 Constructing Liapunov Functions.- 8.5 Conditions of Absolute Stability.- 9 The Frequency Method of Stability Analysis.- 9.1 Introduction.- 9.2 Transfer Functions and Frequency Characteristics.- 9.3 The Nyquist Stability Criterion for a Linear System.- 9.4 Stability of Continuously Nonlinear Systems.- 9.5 Examples.- 9.6 Problems.- References.