Mechanical Systems, Classical Models: Volume 3: Analytical Mechanics

ISBN-13: 9789400736832 / Angielski / Miękka / 2012 / 772 str.

Petre P. Teodorescu

Opis

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 role. 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."

Recenzje

From the reviews:

"The present one deals with analytical mechanics. ... The presentation of material is carefully thought out and combines the exactness, completeness and simplicity that helps in understanding of the material. A particular impression makes the rich bibliography and the completeness of author's scope. This book is one of the best modern courses on analytical mechanics ... . Undoubtedly, this course will be useful for scientists, engineers, teachers and students." (Alexander Mikhailovich Kovalev, Zentralblatt MATH, Vol. 1177, 2010)

Spis treści

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.

O autorze

Prof. Dr. Doc. Petre P. Teodorescu
Born: June 30, 1929, Bucuresti.
M.Sc.: Faculty of Mathematics of the University of Bucharest, 1952; Faculty of Bridges of the Technical University of Civil Engineering, Bucharest, 1953.
Ph.D.: "Calculus of rectangular deep beams in a general case of support and loading", Technical University of Civil Engineering, Bucharest, 1955.
Academic Positions: Consulting Professor.
at the University of Bucharest, Faculty of Mathematics.
Fields of Research: Mechanics of Deformable Solids (especially Elastic Solids), Mathematical Methods of Calculus in Mechanics.
Selected Publications:
1. "Applications of the Theory of Distributions in Mechanics", Editura Academiei-Abacus Press, Bucuresti-Tunbrige Wells, Kent, 1974 (with W. Kecs);
2. "Dynamics of Linear Elastic Bodies", Editura Academiei-Abacus Press, Bucuresti-Tunbrige Wells, Kent, 1975;
3. "Spinor and Non-Euclidean Tensor Calculus with Applications", Editura Tehnicã-Abacus Press, Bucuresti-Tunbrige Wells, Kent, 1983 (with I. Beju and E. Soos);
4. "Mechanical Systems", vol. I, II, Editura Tehnicã, Bucuresti, 1988.
Invited Addresses: The 2nd European Conference of Solid Mechanics, September 1994, Genoa, Italy: Leader of a Section of the Conference and a Communication.
Lectures Given Abroad: Hannover, Dortmund, Paderborn, Germany, 1994; Padova, Pisa, Italy, 1994.
Additional Information: Prize "Gh. Titeica" of the Romanian Academy in 1966; Member in the Advisory Board of Meccanica (Italy), Mechanics Research Communications and Letters in Applied Engineering Sciences (U.S.A.); Member of GAMM (Germany) and AMS (U.S.A.); Reviewer: Mathematical Reviews, Zentralblatt fuer Mathematik und ihre Grenzgebiete, Ph.D. advisor.

Blurb

This third volume completes the Work Mechanical Systems, Classical Models. The first two volumes dealt with particle dynamics and with discrete and continuous mechanical systems. The present volume studies analytical mechanics. Topics like Lagrangian and Hamiltonian mechanics, the Hamilton-Jacobi method, and a study of systems with separate variables are thoroughly discussed. Also included are variational principles and canonical transformations, integral invariants and exterior differential calculus, and particular attention is given to non-holonomic mechanical systems.
The author explains in detail all important aspects of the science of mechanics, regarded as a natural science, and shows how they are useful in understanding important natural phenomena and solving problems of interest in applied and engineering sciences.
Professor Teodorescu has spent more than fifty years as a Professor of Mechanics at the University of Bucharest and this book relies on the extensive literature on the subject as well as the author's original contributions.

Audience: scientists and researchers in applied mathematics, physics and engineering.