Foundations of Mechanics book cover

Foundations of Mechanics

In the last three decades the field of mechanics has seen spectacular progress due to the demand for applications in problems of cosmology, thermonuclear fusion, metallurgy, etc. This book provides a broad and thorough overview on the foundations of mechanics. It discusses theoretical mechanics and continuum mechanics, as well as phenomenological thermodynamics, quantum mechanics and relativistic mechanics. Each chapter presents the basic physical facts of interest without going into details and derivations and without using advanced mathematical formalism. The first part constitutes a classical exposition of Lagrange's and Hamilton's analytical mechanics on which most of the continuum theory is based. The section on continuum mechanics focuses mainly on the axiomatic foundations, with many pointers for further research in this area. Special attention is given to modern continuum thermodynamics, both for the foundations and applications. A section on quantum mechanics is also included, since the phenomenological description of various quantum phenomena is becoming of increasing importance. The work will prove indispensable to engineers wishing to keep abreast of recent theoretical advances in their field, as well as initiating and guiding future research.

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Published: April 1992

Imprint: Elsevier

ISBN: 978-0-444-98700-6

Contents

  • Parts: I. Analytical Mechanics (R. Gutowski). 1. Constrained mechanical system. 2. Variational principles of mechanics. 3. Equations of motion of mechanical systems in Lagrange variables and quasi-coordinates. 4. Equations of motion of material systems in canonical variables. 5. Canonical transformations. 6. Integral invariants and conservation laws. II. Relativistic Mechanics (S.L. Bazański). 1. Physical origin of the special theory of relativity. 2. Galilean space-time. 3. Basic space-time concepts of the special theory of relativity. 4. Minkowski space-time. 5. Relativistic kinematics. 6. Dynamics of a material point. 7. Conservation principles. 8. Equations of motion. 9. Canonical formalism. 10. Comments on the relativistic many-body problem. III. Quantum Mechanics (J. Slawianowski). 1. Basic concepts of quantum mechanics. Historical origins. 2. Quantum mechanics of a material point. Wave mechanics. 3. General formulation of quantum mechanics and examples. 4. Simple applications of quantum mechanics. 5. Some approximate methods and their applications. IV. Mechanics of Continuous Media (C. Woźniak). 1. Basic concepts. 2. Fundamental principles. 3. Investigation of the balance principles. 4. General field equations. 5. Materials. 6. Constraints and loadings. 7. Specialized theories. V. Phenomenological Thermodynamics (K. Wilmański). 1. Introduction. 2. Fundamentals of abstract phenomenological thermodynamics. 3. Thermodynamics of thermomechanical materials. 4. Comments on the second law of thermodynamics. Bibliography. Subject Index.

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