Kooperativer Bibliotheksverbund

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Umfang: XV, 474 p. 187 illus., 6 illus. in color. , online resource.

Ausgabe: 1st ed. 2021.

ISBN: 9783030641184

Serie: Foundations of Engineering Mechanics,

Inhalt: Available for the first time in English, this two-volume course on theoretical and applied mechanics has been honed over decades by leading scientists and teachers, and is a primary teaching resource for engineering and maths students at St. Petersburg University. The course addresses classical branches of theoretical mechanics (Vol. 1), along with a wide range of advanced topics, special problems and applications (Vol. 2). Among the special applications addressed in this second volume are: stability of motion, nonlinear oscillations, dynamics and statics of the Stewart platform, mechanics under random forces, elements of control theory, relations between nonholonomic mechanics and the control theory, vibration and autobalancing of rotor systems, physical theory of impact, statics and dynamics of a thin rod. This textbook is aimed at students in mathematics and mechanics and at post-graduates and researchers in analytical mechanics.

Anmerkung: SECTION III. DYNAMICS.SOME APPLIED PROBLEMS OF THEORETICAL MECHANICS -- Introduction -- Stability of motion -- Nonlinear oscillations -- Dynamics and statics of a Stewart platform -- Vibrations and autobalancing of rotor systems -- Motion control -- Nonholonomic mechanics and control theory -- Mechanics with random forces -- Physical impact theory -- Statics and dynamics of a thin rod -- Flight dynamics.

In: Springer Nature eBook

Weitere Ausg.: Printed edition: ISBN 9783030641177

Weitere Ausg.: Printed edition: ISBN 9783030641191

Weitere Ausg.: Printed edition: ISBN 9783030641207

Sprache: Englisch

DOI: 10.1007/978-3-030-64118-4

URL: https://doi.org/10.1007/978-3-030-64118-4

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Umfang: 1 online resource (481 pages)

ISBN: 3-030-64118-X

Serie: Foundations of Engineering Mechanics

Anmerkung: Intro -- The Review on the Textbook of the Editor of the Series "Foundations of Engineering Mechanics" of Springer Publishing -- Introduction to the Second Volume -- Contents -- Part III Dynamics. Some Applied Problems of Rational Mechanics -- 1 Stability of Motion -- 1 Differential Equations of Disturbed Motion -- 2 The Direct Lyapunov Method -- 3 Stability of Equilibrium and Stationary Motions of Conservative Systems -- 4 Thompson and Tait's Theorems -- 5 Study of the Stability from the Linear Approximation -- 6 Stability of Periodic Solutions from Consideration of the Linear Approximation -- 7 Oscillations of a Pendulum with a Vibrating Suspension Point. The Mathieu Equation -- 2 Nonlinear Oscillations -- 1 Basic Properties of Nonlinear Systems -- 2 Particular Cases of Nonlinear Oscillations -- 3 Using Gauss' Principle in Searching Approximate Solutions of Equations of Nonlinear Oscillations. The Bubnov-Galerkin Method -- 4 The Small-Parameter Method -- 5 The Krylov-Bogolyubov Method -- 6 The Method of Direct Separation of Motions -- 7 The Two-Scale Expansion Method -- 8 The Duffing Equation and Strange Attractor -- 3 Dynamics and Statics of the Stewart Platform -- 1 Problem Formulation and Kinematics of the Stewart Platform -- 2 Differential Equations of Motion of the Loaded Stewart Platform -- 3 The Effect of the Inertia and Weight of the Pneumatic Cylinders -- 4 Feedback Construction. Motion Stabilization for a Stewart Platform -- 5 Linearization of the Platform Motion Equations -- 6 Workspaces of A Stewart Platform in the Six-Dimensional Space of Generalized Coordinates -- 7 Problem Formulation and Coordinate Systems -- 8 Formulas for Transitions Between Coordinate Frames -- 9 Solution of the Direct Dynamics Problem -- 10 Solution of the Inverse Dynamics Problem -- 11 Vertical Oscillations of the Platform. , 12 On Instability of the Solution of the Inverse Dynamics Problem for the Stewart Platform. Introduction of Feedbacks -- 13 Kinematics of a Three-Rod Stewart Platform -- 14 Dynamics Equations for a Three-Rod Platform -- 15 Stabilization of Equilibrium of the Horizontal Position of the Platform -- 16 A Numerical Example -- 4 Vibrations and Autobalancing of Rotor Systems -- 1 Forced and Self-excited Oscillations of a Rotor with an Isotropic Viscoelastic Shaft -- 2 Forced and Self-excited Oscillations of a Rotor with an Orthotropic Viscoelastic Shaft -- 3 Automatic Balancing of a Statically Unbalanced Rotor -- 4 Automatic Balancing of a Jeffcott Rotor with an Orthotropic Elastic Shaft -- 5 Effect of Design Imperfection of the Automatic Ball Balancer -- 5 Elements of the Motion Control -- 1 Statements of Optimal Control Problems -- 2 Solving the Optimal Control Problem by Methods of the Classical Variational Calculus. The Pontryagin Maximum Principle -- 3 Boundary Conditions -- 4 Solving the Time-Optimal Problem Using the Pontryagin Maximum Principle -- 5 Control of the Horizontal Motion of a Cart with Pendula with the Use of the Pontryagin Maximum Principle -- 6 Linear Problems in the Control Theory. Controllability -- 7 Stabilizability and Observability -- 6 Generalized Chebyshev Problem. Nonholonomic Mechanics and Control Theory -- 1 Formulation of the Generalized Chebyshev Problem -- 2 The First Theory of Motion for Nonholonomic Systems with High-Order Constraints. Construction of a Compatible System of Differential Equations -- 3 Motion of an Artificial Earth Satellite with Constant in Magnitude Acceleration. Dimensional Differential Equations of Motion -- 4 Motion of an Artificial Earth Satellite with Constant Modulo Acceleration. The Dimensionless Differential Motion Equations. , 5 The Second Theory of Motion for Nonholonomic Systems with High-Order Constraints. The Generalized Gauss Principle -- 6 Motion of a Spacecraft with Constant Acceleration via the Second Theory of Motion for Nonholonomic Systems with High-Order Constraints. Dimensional Differential Equations -- 7 Spacecraft Motion with Constant Accelerations via the Second Theory of Motion for Nonholonomic Systems with High-Order Constraints. The Dimensionless Differential Equations -- 8 Formulation of One of the Most Important Problems of Control Theory -- 9 Relation Between a Solution Obtained via the Pontryagin Maximum Principle and the Nonholonomic Problem -- 10 Solution of the Problem via the Generalized Gauss Principle -- 11 The Extended (Generalized) Boundary-Value Problem -- 12 Singular Points of the Solution -- 13 Construction of an Analytic Solution of the Problem Free From Singular Points -- 14 Another Approach to the Problem of Oscillation Suppression of a Cart with Two Pendula -- 15 Suppression of Horizontal Oscillations of a Three-Mass System with Springs -- 16 Suppression of Oscillations of a Cantilever -- 7 Mechanics with Random Forces -- 1 Elements of Probability Theory -- 2 Multivariate Random Variables -- 3 Random Processes -- 4 Calculus of Random Variables and Random Processes -- 5 Mechanical System with One Degree of Freedom Subject to a Random Force -- 6 Correlation Analysis of a Linear Mechanical System with Several Degrees of Freedom -- 7 Stationary Random Processes -- 8 The Spectral Density -- 9 The Spectral Decomposition of a Stationary Process -- 10 Oscillations of a Mechanical System with One Degree of Freedom Under Stationary Random Perturbation -- 11 Oscillations of a Mechanical System with Several Degrees of Freedom Under a Stationary Random Perturbation -- 12 Nonlinear and Statistically Nonlinear Problems. , 13 Markov Processes. The Fokker-Planck-Kolmogorov (FPK) Equation -- 8 Physical Impact Theory -- 1 Central Impact of Two Bodies -- 2 Application of General Theorems of Dynamics to the Study of Collisions of Solids -- 3 Impact Theory of Mechanical Systems with Ideal Constraints -- 9 Statics and Dynamics of Thin Rod -- 1 Introduction -- 2 Axial Vibration of Rod. Linear Approximation -- 3 Bending and Transverse Vibration of Rod -- 4 Classical Solutions of Euler and Lavrentiev-Ishlinsky -- 5 Axial-Transverse Vibration. Linear Approximation -- 6 Parametric Resonances -- 7 Instability at Load Less Than Euler Load -- 8 Quasilinear Approximation -- 9 Asymptotic Integration of Quasilinear Equation of Rod Motion -- 10 Post-Critical Deformation of Rod -- 11 Axial Body Impact on the Rod -- 10 Flight Dynamics -- 1 Basic Coordinate Systems Used in Flight Dynamics. Kinematic Equations of Motion -- 2 The Motion Equation of an Aircraft in the Body-Axes System -- 3 Forces Acting on an Aircraft -- 4 Motion of a Systems of Variable Mass. Thrust of a Jet Engine -- 5 Motion of an Aircraft in the Launch Coordinate System -- 6 Application of Methods of Nonholonomic Mechanics for Aircraft Targeting -- Index.

Weitere Ausg.: Print version: Polyakhov, Nikolai Nikolaevich Rational and Applied Mechanics Cham : Springer International Publishing AG,c2022 ISBN 9783030641177

Sprache: Englisch