The Variational Principles of Mechanics by Cornelius Lanczos (English) Paperback

Description: The Variational Principles of Mechanics by Cornelius Lanczos, Physics Philosophic, less formalistic approach to analytical mechanics offers model of clear, scholarly exposition at graduate level with coverage of basics, calculus of variations, principle of virtual work, equations of motion, more. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description Analytical mechanics is, of course, a topic of perennial interest and usefulness in physics and engineering, a discipline that boasts not only many practical applications, but much inherent mathematical beauty. Unlike many standard textbooks on advanced mechanics, however, this present text eschews a primarily technical and formalistic treatment in favour of a fundamental, historical, philosophical approach. As the author remarks, there is a tremendous treasure of philosophical meaning"" behind the great theories of Euler and Lagrange, Hamilton, Jacobi, and other mathematical thinkers.Well-written, authoritative, and scholarly, this classic treatise begins with an introduction to the variational principles of mechanics including the procedures of Euler, Lagrange, and Hamilton. Ideal for a two-semester graduate course, the book includes a variety of problems, carefully chosen to familiarize the student with new concepts and to illuminate the general principles involved. Moreover, it offers excellent grounding for the student of mathematics, engineering, or physics who does not intend to specialize in mechanics, but wants a thorough grasp of the underlying principles.The late Professor Lanczos (Dublin Institute of Advanced Studies) was a well-known physicist and educator who brought a superb pedagogical sense and profound grasp of the principles of mechanics to this work, now available for the first time in an inexpensive Dover paperback edition. His book will be welcomed by students, physicists, engineers, mathematicians, and anyone interested in a clear masterly exposition of this all-important discipline. Table of Contents Introduction 1. The variational approach to mechanics 2. The procedure of Euler and Lagrange 3. Hamiltons procedure 4. The calculus of variations 5. Comparison between the vectorial and the variational treatments of mechanics 6. Mathematical evaluation of the variational principles 7. Philosophical evaluation of the variational approach to mechanics I. The Basic Concepts of Analytical Mechanics 1. The Principal viewpoints of analytical mechanics 2. Generalized coordinates 3. The configuration space 4. Mapping of the space on itself 5. Kinetic energy and Riemannian geometry 6. Holonomic and non-holonomic mechanical systems 7. Work function and generalized force 8. Scleronomic and rheonomic systems. The law of the conservation of energy II. The Calculus of Variations 1. The general nature of extremum problems 2. The stationary value of a function 3. The second variation 4. Stationary value versus extremum value 5. Auxiliary conditions. The Lagrangian lambda-method 6. Non-holonomic auxiliary conditions 7. The stationary value of a definite integral 8. The fundamental processes of the calculus of variations 9. The commutative properties of the delta-process 10. The stationary value of a definite integral treated by the calculus of variations 11. The Euler-Lagrange differential equations for n degrees of freedom 12. Variation with auxiliary conditions 13. Non-holonomic conditions 14. Isoperimetric conditions 15. The calculus of variations and boundary conditions. The problem of the elastic bar III. The principle of virtual work 1. The principle of virtual work for reversible displacements 2. The equilibrium of a rigid body 3. Equivalence of two systems of forces 4. Equilibrium problems with auxiliary conditions 5. Physical interpretation of the Lagrangian multiplier method 6. Fouriers inequality IV. DAlemberts principle 1. The force of inertia 2. The place of dAlemberts principle in mechanics 3. The conservation of energy as a consequence of dAlemberts principle 4. Apparent forces in an accelerated reference system. Einsteins equivalence hypothesis 5. Apparent forces in a rotating reference system 6. Dynamics of a rigid body. The motion of the centre of mass 7. Dynamics of a rigid body. Eulers equations 8. Gauss principle of least restraint V. The Lagrangian equations of motion 1. Hamiltons principle 2. The Lagrangian equations of motion and their invariance relative to point transformations 3. The energy theorem as a consequence of Hamiltons principle 4. Kinosthenic or ignorable variables and their elimination 5. The forceless mechanics of Hertz 6. The time as kinosthenic variable; Jacobis principle; the principle of least action 7. Jacobis principle and Riemannian geometry 8. Auxiliary conditions; the physical significance of the Lagrangian lambda-factor 9. Non-holonomic auxiliary conditions and polygenic forces 10. Small vibrations about a state of equilibrium VI. The Canonical Equations of motion 1. Legendres dual transformation 2. Legendres transformation applied to the Lagrangian function 3. Transformation of the Lagrangian equations of motion 4. The canonical integral 5. The phase space and the space fluid 6. The energy theorem as a consequence of the canonical equations 7. Liouvilles theorem 8. Integral invariants, Helmholtz circulation theorem 9. The elimination of ignorable variables 10. The parametric form of the canonical equations VII. Canonical Transformations 1. Coordinate transformations as a method of solving mechanical problems 2. The Lagrangian point transformations 3. Mathieus and Lies transformations 4. The general canonical transformation 5. The bilinear differential form 6. The bracket expressions of Lagrange and Poisson 7. Infinitesimal canonical transformations 8. The motion of the phase fluid as a continuous succession of canonical transformations 9. Hamiltons principal function and the motion of the phase fluid VIII. The Partial differential equation of Hamilton-Jacobi 1. The importance of the generating function for the problem of motion 2. Jacobis transformation theory 3. Solution of the partial differential equation by separation 4. Delaunays treatment of separable periodic systems 5. The role of the partial differential equation in the theories of Hamilton and Jacobi 6. Construction of Hamiltons principal function with the help of Jacobis complete solution 7. Geometrical solution of the partial differential equation. Hamiltons optico-mechanical analogy 8. The significance of Hamiltons partial differential equation in the theory of wave motion 9. The geometrization of dynamics. Non-Riemannian geometrics. The metrical significance of Hamiltons partial differential equation IX. Relativistic Mechanics 1. Historical Introduction 2. Relativistic kinematics 3. Minkowskis four-dimensional world 4. The Lorentz transformations 5. Mechanics of a particle 6. The Hamiltonian formulation of particle dynamics 7. The potential energy V 8. Relativistic formulation of Newtons scalar theory of gravitation 9. Motion of a charged particle 10. Geodesics of a four-dimensional world 11. The planetary orbits in Einsteins gravitational theory 12. The gravitational bending of light rays 13. The gravitational red-shirt of the spectral lines Bibliography X. Historical Survey XI. Mechanics of the Continua 1. The variation of volume integrals 2. Vector-analytic tools 3. Integral theorems 4. The conservation of mass 5. Hydrodynamics of ideal fluids 6. The hydrodynamic equations in Lagrangian formulation 7. Hydrostatics 8. The circulation theorem 9. Eulers form of the hydrodynamic equations 10. The conservation of energy 11. Elasticity. Mathematical tools 12. The strain tensor 13. The stress tensor 14. Small elastic vibrations 15. The Hamiltonization of variational problems 16. Youngs modulus. Poissons ratio 17. Elastic stability 18. Electromagnetism. Mathematical tools 19. The Maxwell equations 20. Noethers principle 21. Transformation of the coordinates 22. The symmetric energy-momentum tensor 23. The ten conservation laws 24. The dynamic law in field theoretical derivation Appendix I; Appendix II; Bibliography; Index Long Description Philosophic, less formalistic approach to perennially important field of analytical mechanics. Model of clear, scholarly exposition at graduate level with coverage of basic concepts, calculus of variations, principle of virtual work, equations of motion, relativistic mechanics, much more. First inexpensive paperbound edition. Index. Bibliography. Details ISBN0486650677 Author Physics Short Title VARIATIONAL PRINCIPLES OF MECH Pages 418 Language English Edition 4th ISBN-10 0486650677 ISBN-13 9780486650678 Media Book Format Paperback Series Number 4 Imprint Dover Publications Inc. Place of Publication New York Country of Publication United States Birth 1893 Death 1974 Illustrations Illustrations, unspecified DOI 10.1604/9780486650678 UK Release Date 1986-09-22 AU Release Date 1986-09-22 NZ Release Date 1986-09-22 Publisher Dover Publications Inc. Edition Description New edition Series Dover Books on Physics DEWEY 531 Audience Undergraduate Year 2003 Publication Date 2003-03-28 US Release Date 2003-03-28 We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:97852040;

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