Movement Equations 4 Equilibriums and Small Movements [Hardcover]

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.

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 Os  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&llÃ-