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Foundations of Mechanics.

Author: Stanislaw Bazanski; H Zorski
Publisher: Burlington : Elsevier Science, 1992.
Series: Studies in applied mechanics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bazanski, Stanislaw.
Foundations of Mechanics.
Burlington : Elsevier Science, ©1992
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Stanislaw Bazanski; H Zorski
ISBN: 9781483291611 1483291618
OCLC Number: 895436472
Notes: 2.3 Galilean transformations.
Description: 1 online resource (614 pages).
Contents: Front Cover; Foundations of Mechanics; Copyright Page; Preface; Table of Contents; Part I: Analytical Mechanics (Roman Gutowski); Chapter 1. Constrained mechanical systems; 1.1 Constrained and free mechanical systems; 1.2 Holonomic, non-holonomic, scleronomous, and rheonomous constraints; 1.3 Extending the concept of constraints. Constraints in controlled mechanical systems; Chapter 2. Variational principles of mechanics; 2.1 Virtual displacements; 2.2 Ideal constraints; 2.3 D'Alembert's principle, Jourdain's principle, and Gauss's principle. 2.4 The principle of virtual work and the foundations of analytical statics2.5 Construction of equations of motion of mechanical systems based on differential variational principles; 2.6 Generalized coordinates and velocities and quasi-coordinates and quasi-velocities; 2.7 Hamilton's principle; 2.8 Asynchronous variation. The Maupertuis-Lagrange principle; Chapter 3. Equations of motion of mechanical systems in Lagrange variables and quasi-coordinates; 3.1 Lagrange equations of the second kind for holonomic systems; 3.2 The energy of a system in generalized coordinates. 3.3 Lagrange's equations of the second kind in the form of ordinary differential equations. Invariance of Lagrange's equations of the second kind3.4 Boltzmann-Hamel equations for holonomic systems in quasi-coordinates; 3.5 Equations of motion for non-holonomic systems in generalized coordinates and quasi-coordinates; Chapter 4. Equations of motion of material systems in canonical variables; 4.1 Canonical variables. Hamilton's function; 4.2 Equations of motion of holonomic systems in canonical variables; 4.3 Equations of motion of non-holonomic systems in canonical variables. 4.4 The Hamilton-Jacobi method of investigating the motion of material systems, and its connection with the canonical equations of motionChapter 5. Canonical transformations; 5.1 Finite and infinitely small canonical transformations; 5.2 The connection between canonical transformations and the Hamilton-Jacobi theory; Chapter 6. Integral invariants and conservation laws; 6.1 Systems of differential equations of motion which have integral invariants; 6.2 The relationship between integral invariants and canonical transformations. 6.3 Phase fluid and the hydrodynamic interpretation of integral invariants6.4 Conservation laws in classical mechanics. The Noether theorem; Bibliography; Part II: Relativistic Mechanics (Stanislaw Leon Bazanski), ; Chapter 1. Physical origin of the special theory of relativity; 1.1 Development of early ideas about time and space; 1.2 The Michelson-Morley experiment; 1.3 Aberration; 1.4 Fizeau's experiment; 1.5 Precursors of new views on time and space; 1.6 The approach proposed by Einstein; Chapter 2. Galilean space-time; 2.1 Fundamental assumptions; 2.2 The structure of space-time.
Series Title: Studies in applied mechanics.

Abstract:

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 classic.

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