Mechanical Systems, Classical Models (eBook)
X, 772 Seiten
Springer Netherlands (Verlag)
978-90-481-2764-1 (ISBN)
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.
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 role. 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.
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 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.
Contents 6
Preface 9
18 Lagrangian Mechanics 11
18.1 Preliminary Results 12
18.2 Lagrange’s Equations 55
18.3 Other Problems Concerning Lagrange’s Equations 93
19 Hamiltonian Mechanics 125
19.1 Hamilton’s Equations 125
19.2 The Hamilton–Jacobi method 170
20 Variational Principles. Canonical Transformations 223
20.1 Variational Principles 223
20.2 Canonical Transformations 275
20.3 Symmetry Transformations. Noether’s Theorem. Conservation Laws 310
21 Other Considerations on Analytical Methods in Dynamics of Discrete Mechanical Systems 344
21.1. Integral Invariants. Ergodic Theorems 344
21.2 Periodic Motions. Action-Angle Variables 365
21.3 Methods of Exterior Differential Calculus. Elements of Invariantive Mechanics 377
21.4 Formalisms in the Dynamics of Mechanical Systems 399
21.5 Control Systems 411
22 Dynamics of Non-holonomic Mechanical Systems 420
22.1 Kinematics of Non-holonomic Mechanical Systems 420
22.2 Lagrange’s Equations. Other Equations of Motion 439
22.3 Gibbs–Appell equations 487
22.4 Other Problems on the Dynamics of Non-holonomic Mechanical Systems 500
23 Stability and Vibrations 514
23.1 Stability of Mechanical Systems 514
23.2. Vibrations of Mechanical Systems 575
24 Dynamical Systems. Catastrophes and Chaos 638
24.1 Continuous and Discrete Dynamical Systems 639
24.2 Elements of the Theory of Catastrophes 691
24.3 Periodic Solutions. Global Bifurcations 706
24.4 Fractals. Chaotic Motions 721
BIBLIOGRAPHY 748
Subject Index 768
Name Index 774
| Erscheint lt. Verlag | 30.9.2009 |
|---|---|
| Reihe/Serie | Mathematical and Analytical Techniques with Applications to Engineering |
| Zusatzinfo | X, 772 p. |
| Verlagsort | Dordrecht |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Naturwissenschaften ► Physik / Astronomie ► Mechanik | |
| Technik | |
| Schlagworte | analytical methods in mechanical systems • Applied mathematics • Dynamics • dynamics of mechanical systems • Lagrangian mechanics • MB09 • Mechanics |
| ISBN-10 | 90-481-2764-5 / 9048127645 |
| ISBN-13 | 978-90-481-2764-1 / 9789048127641 |
| Haben Sie eine Frage zum Produkt? |
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