Movement equations. 4, Equilibriums and small movements / Michel Borel and Georges Vebuzelos.

Format:

Book

Author/Creator:

Borel, Michel, author.

Vebuzelos, Georges, author.

Language:

English

Subjects (All):

Equilibrium.

Motion.

Physical Description:

1 online resource (249 pages)

Edition:

1st ed.

Place of Publication:

Hoboken, New Jersey : Wiley Blackwell, 2018.

Summary:

An important instance of the application of unbuckled solid mechanics is that of its stability and small movements from this situation. The problem expressing goes through the linearization of the movement equations set up in the 3rd volume of this treaty, by their limited development. This book gives and develops the process which leads to the differential linear equations expressing this kind of movement and allowing the study of the equilibrium and the stability of an unbuckled solid.

Contents:

Cover

Half-Title Page

Title Page

Copyright Page

Contents

Introduction

Table of Notations

1. Equilibrium, Stationary Movement and Oscillation of a Free Solid

1.1. Expression of the fundamental principle of dynamics for a free solid

1.2. Canonical form of the fundamental principle

1.2.1. Dynamic resultant

1.2.2. Dynamic moment at OS

1.2.3. Fundamental principle of dynamics

1.3. Equilibrium of the free solid

1.3.1. Equations of equilibrium

1.3.2. Stability of equilibrium

1.4. General equations of small movements of a free solid

1.4.1. Reminder of developments limited to the first order

1.4.2. Equations of small movements of the free solid

1.4.3. Analytical mechanics of free solids

1.5. Matrix expression of small movements of a free solid

1.5.1. Using vector representation

1.5.2. Using analytical mechanics

1.5.3. Relative situation of frames at the equilibrium

1.6. Stationary movement

1.6.1. Cyclic parameters

1.6.2. Characterizing a stationary movement

1.6.3. Conditions of realization of a stationary movement

1.6.4. Neighboring motions and stability of a stationary movement

1.6.5. Applications

2. Solving Equations of Small Movements

2.1. Linear differential systems with constant coefficients

2.1.1. General periodic solution of the homogeneous system

2.1.2. Particular solution to the system

2.1.3. Exercise 1

2.2. Laplace transformation

2.2.1. Definition

2.2.2. Linearity of a Laplace transformation

2.2.3. Laplace transforms for common functions

2.2.4. Functional properties of the Laplace transformation

2.2.5. Examples of use of the Laplace transform

2.2.6. Applications

3. Oscillator Studies

3.1. Physical nature of oscillatory motion

3.2. The single oscillator

3.2.1. Definitions.

3.2.2. Conditions of an oscillatory motion

3.2.3. Study of free oscillatory motion

3.2.4. Study of forced oscillations

3.2.5. Study of a modulated oscillatory signal

3.3. Motion of coupled oscillators

3.3.1. Coupling of two oscillators

3.3.2. Study of free oscillation

3.3.3. Applications: problem 6

3.4. Oscillatory device of k oscillators - equilibrium and stability

3.4.1. Approaching the problem

3.4.2. Routh criteria

4. Gyroscopic Motion

4.1. Gyroscopic coupling

4.1.1. Composition of the device

4.1.2. Velocity-distributing torsor

4.1.3. Kinetic energies of all three components

4.1.4. Equations of dynamics

4.1.5. Equations of analytical mechanics

4.1.6. Situations of equilibrium of the gyroscopic device

4.1.7. Stability of the stationary movement

4.2. Gyroscopic pendulum

4.2.1. Composition of the device

4.2.2. Velocity-distributing torsors

4.2.3. Kinetic energies

4.2.4. Lagrange equations

4.2.5. Equilibrium and stability

4.3. The gyro-compass

4.3.1. Composition of the device

4.3.2. Fundamental principle of dynamics

4.3.3. Equations of analytical mechanics

4.3.4. Stationary movement and stability

4.3.5. Note for establishing Lagrange equations

4.4. Applications: problem 7 - motion stabilizer

Bibliography

Index

Other titles from iSTE in Mechanical Engineering and Solid Mechanics

EULA.

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (EBC, viewed March 8, 2018).

ISBN:

9781119510628

1119510627

9781119482673

1119482674

9781119510642

1119510643

OCLC:

1024286993