Rational and applied mechanics. Volume 2, Special problems and applications / Nikolai Nikolaevich Polyakhov, Petr Evgenievich Tovstik, Mikhail Petrovich Yushkov, Sergey Andreevich Zegzhda ; Petr Evgenievich Tovstik, editor.

Format:

Book

Author/Creator:

Polyakhov, Nikolai Nikolaevich.

Contributor:

Tovstik, Petr Evgenievich, editor.

Yushkov, Mikhail Petrovich.

Zegzhda, S. A. (Sergeĭ Andreevich) (Writer on Mechanics)

Alimov, A. R.

Belkind, E. L.

Belyaev, A. K.

Kovachev, A. S.

Lisachenko, D. A.

Shelkovina, V. A.

Series:

Foundations of engineering mechanics

Language:

English

Subjects (All):

Mechanics.

Mechanics, Applied.

Genre:

Electronic books.

Physical Description:

1 online resource (481 pages).

Other Title:

Special problems and applications

Place of Publication:

Cham, Switzerland : Springer, [2022]

System Details:

text file

Summary:

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.

Contents:

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

Notes:

5 Control of the Horizontal Motion of a Cart with Pendula with the Use of the Pontryagin Maximum Principle.

Other Format:

Print version: Polyakhov, Nikolai Nikolaevich Rational and Applied Mechanics

ISBN:

9783030641184

303064118X

OCLC:

1288211394

Access Restriction:

Restricted for use by site license.