Mechanical Systems, Classical Models

by Teodorescu, Petre P.

• ISBN13: 9781402054419
• ISBN10: 1402054416
• Format: Hardcover
• Copyright: 2007-06-30
• Publisher: Springer Verlag

Summary

All phenomena in nature are characterized by motion; this is an essential property of matter, having infinitely many aspects. Motion can be mechanical, physical, chemical or biological, leading to various sciences of nature, mechanics being one of them. 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 was 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; on the other hand, we must observe that mechanics also influenced the introduction and the development of many mathematical notions. In this respect, the guideline of the present book is precisely the mathematical model of mechanics. A special accent is put on the solving methodology as well as on the mathematical tools used; vectors, tensors and notions of field theory. Continuous and discontinuous phenomena, various mechanical magnitudes are presented in a unitary form by means of the theory of distributions. Some appendices give the book an autonomy with respect to other works, special previous mathematical knowledge being not necessary. Some applications connected to important phenomena of nature are presented, and this also gives one the possibility to solve problems of interest from the technical, engineering point of view. In this form, the book becomes - we dare say - a unique outline of the literature in the field; the author wishes to present the most important aspects connected with the study of mechanical systems, mechanics being regarded as a science of nature, as well as its links to other sciences of nature. Implications in technical sciences are not neglected.

Author Biography

Prof. Dr. Doc. Petre P. TeodorescuBorn: 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 Tehnic+â-ú-Abacus Press, Bucuresti-Tunbrige Wells, Kent, 1983 (with I. Beju and E. Soos);4. "Mechanical Systems", vol. I, II, Editura Tehnic+â-ú, 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.

Table of Contents

Newtonian model of mechanics	p. 1
Mechanics of the systems of forces	p. 75
Mass geometry, displacements, constraints	p. 115
Statistics	p. 201
Kinematics	p. 287
Dynamics of the particle with respect to an internal frame of reference	p. 353
Problems of dynamics of the particle	p. 401
Dynamics of the particle in a field of elastic forces	p. 469
Newtonian theory of universal attraction	p. 543
Other consideration on particle dynamics
Elements of vector calculus	p. 693
Notions of field theory	p. 709
Elements of theory of distributions	p. 731
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