Mechanical Systems, Classical Models PDF Download
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Author: Petre P. Teodorescu
Publisher: Springer Science & Business Media
ISBN: 9048127645
Category : Science
Languages : en
Pages : 781
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Book Description
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.
Author: Petre P. Teodorescu
Publisher: Springer Science & Business Media
ISBN: 9048127645
Category : Science
Languages : en
Pages : 781
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Book Description
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.
Author: Iulian Beju
Publisher: CRC Press
ISBN: 9780856263309
Category : Mathematics
Languages : en
Pages : 316
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Book Description
Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 116
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Book Description
Author: L.R. Shorter
Publisher: Courier Corporation
ISBN: 0486780813
Category : Mathematics
Languages : en
Pages : 372
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Book Description
"A handy book like this," noted The Mathematical Gazette, "will fill a great want." Devoted to fully worked out examples, this unique text constitutes a self-contained introductory course in vector analysis for undergraduate and graduate students of applied mathematics. Opening chapters define vector addition and subtraction, show how to resolve and determine the direction of two or more vectors, and explain systems of coordinates, vector equations of a plane and straight line, relative velocity and acceleration, and infinitely small vectors. The following chapters deal with scalar and vector multiplication, axial and polar vectors, areas, differentiation of vector functions, gradient, curl, divergence, and analytical properties of the position vector. Applications of vector analysis to dynamics and physics are the focus of the final chapter, including such topics as moving rigid bodies, energy of a moving rigid system, central forces, equipotential surfaces, Gauss's theorem, and vector flow. Dover (2014) republication of Introduction to Vector Analysis, originally published by Macmillan and Company, Ltd., London, 1931. See every Dover book in print at www.doverpublications.com
Author: James Henry Taylor
Publisher:
ISBN:
Category :
Languages : en
Pages : 200
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Book Description
Author: Jan Arnoldus Schouten
Publisher: Springer Science & Business Media
ISBN: 3662129272
Category : Mathematics
Languages : en
Pages : 535
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Book Description
This is an entirely new book. The first edition appeared in 1923 and at that time it was up to date. But in 193 5 and 1938 the author and Prof. D. J. STRUIK published a new book, their Einführung I and li, and this book not only gave the first systematic introduction to the kernel index method but also contained many notions that had come into prominence since 1923. For instance densities, quantities of the second kind, pseudo-quantities, normal Coordinates, the symbolism of exterior forms, the LIE derivative, the theory of variation and deformation and the theory of subprojective connexions were included. Now since 1938 there have been many new developments and so a book on RICCI cal culus and its applications has to cover quite different ground from the book of 1923. Though the purpose remains to make the reader acquainted with RICCI's famous instrument in its modern form, the book must have quite a different methodical structure and quite different applica tions have to be chosen. The first chapter contains algebraical preliminaries but the whole text is modernized and there is a section on hybrid quantities (quantities with indices of the first and of the second kind) and one on the many abridged notations that have been developed by several authors. In the second chapter the most important analytical notions that come before the introduction of a connexion aredealt with in full.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 582
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Book Description
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 1052
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Book Description
Author: Library of Congress. Copyright Office
Publisher: Copyright Office, Library of Congress
ISBN:
Category : American literature
Languages : en
Pages : 2832
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Book Description
Author: Jean-Marc Ginoux
Publisher: World Scientific
ISBN: 9814277142
Category : Mathematics
Languages : en
Pages : 341
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Book Description
This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory ? or the flow ? may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes).In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem.
