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Book Cover
E-book
Author Borel, Michel

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

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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.
Motion.
Motion
equilibrium (structural analysis concept)
motion.
Equilibrium
Motion
Form Electronic book
Author Venizelos, Georges
ISBN 9781119510642
1119510643