Mechanical Systems, Classical Models: Volume 3: Analytical Mechanics / Edition 1

Mechanical Systems, Classical Models: Volume 3: Analytical Mechanics / Edition 1

by Petre P. Teodorescu
     
 

ISBN-10: 9048127637

ISBN-13: 9789048127634

Pub. Date: 07/30/2009

Publisher: Springer Netherlands

All phenomena in nature are characterized by motion. Mechanics deals with the objective laws of mechanical motion of bodies, the simplest form of motion. In the study of a science of nature, mathematics plays an important rôle. Mechanics is the first science of nature which has been expressed in terms of mathematics, by considering various mathematical models,…  See more details below

Overview

All phenomena in nature are characterized by motion. Mechanics deals with the objective laws of mechanical motion of bodies, the simplest form of motion. In the study of a science of nature, mathematics plays an important rôle. Mechanics is the first science of nature which has been expressed in terms of mathematics, by considering various mathematical models, associated to phenomena of the surrounding nature. Thus, its development was influenced by the use of a strong mathematical tool. As it was already seen in the first two volumes of the present book, its guideline is precisely the mathematical model of mechanics. The classical models which we refer to are in fact models based on the Newtonian model of mechanics, that is on its five principles, i.e.: the inertia, the forces action, the action and reaction, the independence of the forces action and the initial conditions principle, respectively. Other models, e.g., the model of attraction forces between the particles of a discrete mechanical system, are part of the considered Newtonian model. Kepler’s laws brilliantly verify this model in case of velocities much smaller then the light velocity in vacuum.

Read More

Product Details

ISBN-13:
9789048127634
Publisher:
Springer Netherlands
Publication date:
07/30/2009
Series:
Mathematical and Analytical Techniques with Applications to Engineering Series
Edition description:
2009
Pages:
772
Product dimensions:
9.21(w) x 6.14(h) x 1.63(d)

Table of Contents

Table of Contents – continued from Volume 1 and 2:
Preface
18. Langrangian Mechanics – 1. Preliminary results; 2. Langrange’s equations; 3. Other problems concerning Lagrange’s equations.
19. Hamiltonian Mechanics – 1. Hamilton’s equations; 2. The Hamilton-Jacobi method.
20. Variational Principles. Canonical Transformations – 1. Variational principles; 2. Canonical transformations; 3. Symmetry transformations. Noether’s theorem. Conservation laws.
21. Other Considerations on Analytical Methods in Dynamics of Discrete Mechanical Systems – 1. Integral invariants. Ergodic theorems; 2. Periodic motions. Action – angle variables; 3. Methods of exterior differential calculus. Elements of invariantive mechanics; 4. Formalisms in the dynamics of mechanical systems; 5. Control systems.
22. Dynamics of Non-Holonomic Mechanical Systems – 1. Kinematics of non-holonomic mechanical systems; 2. Lagrange’s equations. Other equations of motion; 3. Gibbs – Appell equations; 4. Other problems on the dynamics of non-holonomic mechanical systems.
23. Stability and Vibrations – 1. Stability of mechanical systems; 2. Vibrations of mechanical systems.
24. Dynamical Systems. Catastrophes and Chaos – 1. Continuous and discrete dynamical systems; 2. Elements of the theory of catastrophes; 3. Periodic solutions. Global bifurcations; 4. Fractals. Chaotic motions.
References.

Read More

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >