Synopses & Reviews
This second volume of Mechanical Systems, Classical Models, deals with the dynamics of systems consisting of discrete particles as well as continuous systems. While differences between these models are highlighted, the generality of the proofs and corresponding computations yields results that are expressed in a common form for both discrete and continuous 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. A large variety of problems are analyzed, from the traditional to more recent ones, such as the dynamics of rigid solids with variable mass. Professor Teodorescu has spent more that 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: students and researchers in applied mathematics, physics, chemistry, mechanical engineering.
Review
From the reviews: "The second volume deals with mechanical systems of particles ... . General theorems and conservation theorems are given. As one of important applications, the author discusses the problem of n particles. ... As applications, motions of threads and straight bars are studied. ... The book is written clearly ... and its study does not require any special mathematical knowledge. It is intelligible and useful to a large community of scientists, engineers and students." (Boris Ivanovich Konosevich, Zentralblatt MATH, Vol. 1158, 2009)
Synopsis
As it was already seen in the first volume 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, on its five principles, i. e.: the inertia, the forces action, the action and reaction, the parallelogram 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 than the light velocity in vacuum. The non-classical models are relativistic and quantic. Mechanics has as object of study mechanical systems. The first volume of this book dealt with particle dynamics. The present one deals with discrete mechanical systems for particles in a number greater than the unity, as well as with continuous mechanical systems. We put in evidence the difference between these models, as well as the specificity of the corresponding studies; the generality of the proofs and of the corresponding computations yields a common form of the obtained mechanical results for both discrete and continuous systems. We mention the thoroughness by which the dynamics of the rigid solid with a fixed point has been presented. The discrete or continuous mechanical systems can be non-deformable (e. g.
Synopsis
This volume thoroughly details all major aspects of the science of mechanics and shows how they are crucial for understanding important natural phenomena and for solving problems related to applications and engineering.
About the Author
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.
Table of Contents
Volume II. Mechanics of discrete and continuous systems 11: DYNAMICS OF DISCRETE MECHANICAL SYSTEMS 11.1 Dynamics of discrete mechanical systems with respect to an inertial frame of reference. 11.2 Dynamics of discrete mechanical systems with respect to a non-inertial frame of reference. 12: DYNAMICS OF CONTINUOUS MECHANICAL SYSTEMS 12.1 General considerations. 12.2 One-dimensional continuous mechanical systems. 13: OTHER CONSIDERATIONS ON THE DYNAMICS OF MECHANICAL SYSTEMS 13.1 Motions with discontinuities. 13.2 Dynamics of mechanical systems of variable mass. 14: DYNAMICS OF THE RIGID SOLID 14.1 General results. Euler-Poinsot case. 14.2 Case in which the ellipsoid of inertia is of revolution 15: DYNAMICS OF THE RIGID SOLID WITH A FIXED POINT 15.1 General results. Euler-Poinsot case. 15.2 Case in which the ellipsoid of inertia is of rotation. Other cases of integrability. 16: OTHER CONSIDERATIONS ON THE RIGID SOLID 16.1 Motions of the Earth. 16.2 Theory of the gyroscope. 16.3 Dynamics of the rigid solid of variable mass. 17: DYNAMICS OF SYSTEMS OF RIGID SOLIDS 17.1 Motion of systems of rigid solids. 17.2 Motion with discontinuities of the rigid solids. Collision. 17.3 Applications in the dynamics of engines. References; Subject Index; Name Index.