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Book Cover
Author Borel, Michel

Title Movement Equations 4 : Equilibriums and Small Movements
Published Newark : John Wiley & Sons, Incorporated, 2018


Description 1 online resource (249 pages)
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 order1.4.2. 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 Movements2.1. 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. Definitions3.2.2. 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 รข#x80;#x93; 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 components4.1.4. 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
Notes 4.3.5. Note for establishing Lagrange equations
Print version record
Subject Equilibrium.
equilibrium (structural analysis concept)
Form Electronic book
Author Venizelos, Georges
ISBN 9781119510642