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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.
Inhaltsverzeichnis
Newtonian Model of Mechanics.- Mechanics of the Systems of Forces.- Mass Geometry. Displacements. Constraints.- Statics.- Kinematics.- Dynamics of the Particle with Respect to an Inertial Frame of Reference.- Problems of Dynamics of the Particle.- Dynamics of the Particle in a Field of Elastic Forces.- Newtonian Theory of Universal Attraction.- Other Considerations on Particle Dynamics.
Über den Autor / die Autorin
Petre P. Teodorescu is professor at the University of Bucharest and member of the Romanian Academy of Sciences. He is president of the Section of Technical Mechanics and member of GAMM (Gesellschaft für Angewandte Mathematik und Mechanik). He was awarded by a prize of the Romanian Academy and is member of the editorial board of several scientific publications.
Zusammenfassung
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.
Zusatztext
From the reviews:
"This book is the first volume of a treatise on the classical theory of mechanical systems. … The book is useful at the graduate level in physics and mechanical engineering, as well as in mathematics. … The mathematical aspects are carefully presented. The text provides a detailed analysis of some generic examples, which will be enough to show how the theory is applied, at least for experienced readers. The subjects covered by the text are divided into 10 large chapters." (José Fernández-Núñez, Mathematical Reviews, Issue 2008 j)
Bericht
From the reviews:
"This book is the first volume of a treatise on the classical theory of mechanical systems. ... The book is useful at the graduate level in physics and mechanical engineering, as well as in mathematics. ... The mathematical aspects are carefully presented. The text provides a detailed analysis of some generic examples, which will be enough to show how the theory is applied, at least for experienced readers. The subjects covered by the text are divided into 10 large chapters." (José Fernández-Núñez, Mathematical Reviews, Issue 2008 j)
