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Movement Equations 4: Equilibriums and Small Movements - Georges Vénizélos,Bore
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A book in excellent condition. Cover is shiny and undamaged, and the dust jacket is included for hard covers. No missing or damaged pages, no creases or tears, and no underlining/highlighting of text or writing in the margins. May be very minimal identifying marks on the inside cover. Very minimal wear and tear.
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Item specifics
- Condition
- ISBN
- 9781786300355
About this product
Product Identifiers
Publisher
Wiley & Sons, Incorporated, John
ISBN-10
1786300354
ISBN-13
9781786300355
eBay Product ID (ePID)
242732284
Product Key Features
Number of Pages
256 Pages
Language
English
Publication Name
Movement Equations 4 : Equilibriums and Small Movements
Publication Year
2018
Subject
Mechanics / General, Structural
Type
Textbook
Subject Area
Technology & Engineering, Science
Format
Hardcover
Dimensions
Item Height
0.7 in
Item Weight
17.6 Oz
Item Length
9.3 in
Item Width
6.3 in
Additional Product Features
Intended Audience
Scholarly & Professional
Table Of Content
Introduction ix Table of Notations xiii Chapter 1 Equilibrium, Stationary Movement and Oscillation of a Free Solid 1 1.1 Expression of the fundamental principle of dynamics for a free solid 1 1.2 Canonical form of the fundamental principle 4 1.2.1 Dynamic resultant 5 1.2.2 Dynamic moment at O s 5 1.2.3 Fundamental principle of dynamics 7 1.3 Equilibrium of the free solid 7 1.3.1 Equations of equilibrium 7 1.3.2 Stability of equilibrium 9 1.4 General equations of small movements of a free solid 9 1.4.1 Reminder of developments limited to the first order 9 1.4.2 Equations of small movements of the free solid 12 1.4.3 Analytical mechanics of free solids 43 1.5 Matrix expression of small movements of a free solid 59 1.5.1 Using vector representation 60 1.5.2 Using analytical mechanics 63 1.5.3 Relative situation of frames at the equilibrium 65 1.6 Stationary movement 67 1.6.1 Cyclic parameters 67 1.6.2 Characterizing a stationary movement 68 1.6.3 Conditions of realization of a stationary movement 69 1.6.4 Neighboring motions and stability of a stationary movement 71 1.6.5 Applications 74 Chapter 2 Solving Equations of Small Movements 75 2.1 Linear differential systems with constant coefficients 75 2.1.1 General periodic solution of the homogeneous system 77 2.1.2 Particular solution to the system 79 2.1.3 Exercise 1 81 2.2 Laplace transformation 87 2.2.1 Definition 87 2.2.2 Linearity of a Laplace transformation 87 2.2.3 Laplace transforms for common functions 88 2.2.4 Functional properties of the Laplace transformation 91 2.2.5 Examples of use of the Laplace transform 93 2.2.6 Applications 96 Chapter 3 Oscillator Studies 115 3.1 Physical nature of oscillatory motion 115 3.2 The single oscillator 116 3.2.1 Definitions 117 3.2.2 Conditions of an oscillatory motion 117 3.2.3 Study of free oscillatory motion 118 3.2.4 Study of forced oscillations 123 3.2.5 Study of a modulated oscillatory signal 126 3.3 Motion of coupled oscillators 129 3.3.1 Coupling of two oscillators 129 3.3.2 Study of free oscillation 129 3.3.3 Applications: problem 6 138 3.4. Oscillatory device of k oscillators - equilibrium and stability 154 3.4.1 Approaching the problem 154 3.4.2 Routh criteria 155 Chapter 4 Gyroscopic Motion 163 4.1 Gyroscopic coupling 163 4.1.1 Composition of the device 163 4.1.2 Velocity-distributing torsor 166 4.1.3 Kinetic energies of all three components 166 4.1.4 Equations of dynamics 167 4.1.5 Equations of analytical mechanics 168 4.1.6 Situations of equilibrium of the gyroscopic device 172 4.1.7 Stability of the stationary movement 173 4.2 Gyroscopic pendulum 177 4.2.1 Composition of the device 177 4.2.2 Velocity-distributing torsors 178 4.2.3 Kinetic energies 179 4.2.4 Lagrange equations 179 4.2.5 Equilibrium and stability 181 4.3 The gyro-compass 184 4.3.1 Composition of the device 184 4.3.2 Fundamental principle of dynamics 186 4.3.3 Equations of analytical mechanics 186 4.3.4 Stationary movement and stability 193 4.3.5 Note for establishing Lagrange equations 199 4.4 Applications: problem 7 - motion stabilizer 199 Bibliography 213 Index 215
Synopsis
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., The set of books on Non-deformable Solid Mechanics, of which this book is the fourth volume, is an essential tool for those looking to develop a rigorous knowledge of the discipline, whether students, professionals (in search of an approach to a problem they are dealing with), or anyone else interested. This volume builds on the topics of the previous books in that it applies the principles established in the third volume which led to the movement equations. Through an examination of the scalar consequences of the fundamental principle of dynamics, this book identifies the conceivable situations of equilibrium, the conditions for obtaining them and the values of the situation parameters which correspond with them. A special emphasis is placed on the behavior of oscillatory components and their influence on stabilized and stabilizer systems. This book includes a chapter devoted to the formal mathematics of such systems and another to the stabilizer effects of a common device of coupled components: the gyroscope. It goes through the common applications of this device, including the case of the gyroscopic pendulum, chiefly used for controlling satellites, and the gyro-compass as a navigational instrument which helps maintain true north. Book jacket., 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.
LC Classification Number
QA805
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