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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.

Dynamics of a particle -- Mathematical models. --- Mechanics -- Mathematical models. --- Applied Mathematics --- Applied Physics --- Engineering & Applied Sciences --- Mechanics --- Dynamics of a particle --- Mathematical models. --- Particle, Dynamics of a --- Classical mechanics --- Newtonian mechanics --- Physics. --- Applied mathematics. --- Engineering mathematics. --- Mechanics. --- Mathematical Methods in Physics. --- Applications of Mathematics. --- Physics --- Dynamics --- Quantum theory --- Mathematical physics. --- Mathematics. --- Classical Mechanics. --- Math --- Science --- Physical mathematics --- Mathematics --- Engineering --- Engineering analysis --- Mathematical analysis --- Natural philosophy --- Philosophy, Natural --- Physical sciences

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Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation. The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used. This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid. The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University of Bucharest. The construction of mathematical models is made by treating geometry and kinematics of deformation, mechanics of stresses and constitutive laws. Elastic, plastic and viscous properties are thus put in evidence and the corresponding theories are developed. Space problems are treated and various particular cases are taken into consideration. New solutions for boundary value problems of finite and infinite domains are given and a general theory of concentrated loads is built. Anisotropic and non-homogeneous bodies are studied as well. Cosserat type bodies are also modeled. The connection with thermal and viscous phenomena will be considered too. Audience: researchers in applied mathematics, mechanical and civil engineering.

Elasticity -- Problems, exercises, etc. --- Elasticity. --- Structural dynamics. --- Engineering & Applied Sciences --- Applied Mathematics --- Applied Physics --- Strains and stresses. --- Architectural engineering --- Engineering, Architectural --- Stresses and strains --- Elastic properties --- Young's modulus --- Physics. --- Applied mathematics. --- Engineering mathematics. --- Mechanics. --- Mechanics, Applied. --- Applications of Mathematics. --- Appl.Mathematics/Computational Methods of Engineering. --- Theoretical and Applied Mechanics. --- Mathematical Methods in Physics. --- Architecture --- Elastic solids --- Flexure --- Mechanics --- Statics --- Structural analysis (Engineering) --- Deformations (Mechanics) --- Elasticity --- Engineering design --- Graphic statics --- Strength of materials --- Stress waves --- Structural design --- Mathematical physics --- Matter --- Rheology --- Strains and stresses --- Properties --- Mathematics. --- Mechanics, applied. --- Mathematical physics. --- Classical Mechanics. --- Mathematical and Computational Engineering. --- Physical mathematics --- Physics --- Engineering --- Engineering analysis --- Mathematical analysis --- Math --- Science --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Mathematics --- Natural philosophy --- Philosophy, Natural --- Physical sciences

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Mathematics --- Mathematical physics --- Classical mechanics. Field theory --- toegepaste wiskunde --- wiskunde --- fysica --- mechanica

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Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation. The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used. This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid. The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University of Bucharest. The construction of mathematical models is made by treating geometry and kinematics of deformation, mechanics of stresses and constitutive laws. Elastic, plastic and viscous properties are thus put in evidence and the corresponding theories are developed. Space problems are treated and various particular cases are taken into consideration. New solutions for boundary value problems of finite and infinite domains are given and a general theory of concentrated loads is built. Anisotropic and non-homogeneous bodies are studied as well. Cosserat type bodies are also modeled. The connection with thermal and viscous phenomena will be considered too. Audience: researchers in applied mathematics, mechanical and civil engineering.

Mathematics --- Mathematical physics --- Classical mechanics. Field theory --- Physics --- Applied physical engineering --- Engineering sciences. Technology --- analyse (wiskunde) --- toegepaste wiskunde --- toegepaste mechanica --- economie --- wiskunde --- ingenieurswetenschappen --- fysica --- mechanica

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The present book has its source in the authors’ wish to create a bridge between the mathematical and the technical disciplines, which need a good knowledge of a strong mathematical tool. The necessity of such an interdisciplinary work drove the authors to publish a first book to this aim with Editura Tehnica, Bucharest, Romania. The present book is a new, English edition of the volume published in 1999. It contains many improvements concerning the theoretical (mathematical) information, as well as new topics, using enlarged and updated references. Only ordinary differential equations and their solutions in an analytical frame were considered, leaving aside their numerical approach. The problem is firstly stated in its mechanical frame. Then the mathematical model is set up, emphasizing on the one hand the physical magnitude playing the part of the unknown function and on the other hand the laws of mechanics that lead to an ordinary differential equation or system. The solution is then obtained by specifying the mathematical methods described in the corresponding theoretical presentation. Finally a mechanical interpretation of the solution is provided, this giving rise to a complete knowledge of the studied phenomenon. The number of applications was increased, and many of these problems appear currently in engineering. Audience Mechanical and civil engineers, physicists, applied mathematicians, astronomers and students. The prerequisites are courses of elementary analysis and algebra, as given at a technical university. On a larger scale, all those interested in using mathematical models and methods in various fields, like mechanics, civil and mechanical engineering, and people involved in teaching or design will find this work indispensable.

Differential equations. --- Mathematics. --- Math --- Science --- 517.91 Differential equations --- Differential equations --- Global analysis (Mathematics). --- Mechanics. --- Engineering mathematics. --- Differential Equations. --- Analysis. --- Applications of Mathematics. --- Classical Mechanics. --- Mathematical and Computational Engineering. --- Ordinary Differential Equations. --- Engineering --- Engineering analysis --- Mathematical analysis --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematics --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- 517.1 Mathematical analysis