The Variational Principles of Mechanics
Professor Lanczos's book is not a textbook on advances mechanics. Its purpose is to formulate and explain these fundamental concepts of this exact science which started with the work of Galileo and led to the achievements of modern relativity theory and quantum theory.
Saved in:
| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Toronto :
University of Toronto Press,
1949.
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| Series: | Heritage.
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| Online Access: | CONNECT |
MARC
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| 100 | 1 | |a Lanczos, Cornelius. | |
| 245 | 1 | 4 | |a The Variational Principles of Mechanics |
| 260 | |a Toronto : |b University of Toronto Press, |c 1949. | ||
| 300 | |a 1 online resource (395 pages) | ||
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| 505 | 0 | |a Cover; INTRODUCTION; 1. The variational approach to mechanics; 2. The procedure of Euler and Lagrange; 3. Hamilton's 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 | |
| 505 | 8 | |a 4. Equilibrium problems with auxiliary conditions5. Physical interpretation of the Lagrangian multiplier method; 6. Fourier's inequality; IV. D'ALEMBERT'S PRINCIPLE; 1. The force of inertia; 2. The place of d'Alembert's principle in mechanics; 3. The conservation of energy as a consequence of d'Alembert's principle; 4. Apparent forces in an accelerated reference system. Einstein's 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. Euler's equations | |
| 500 | |a 9. Non-holonomic auxiliary conditions and polygenic forces | ||
| 520 | |a Professor Lanczos's book is not a textbook on advances mechanics. Its purpose is to formulate and explain these fundamental concepts of this exact science which started with the work of Galileo and led to the achievements of modern relativity theory and quantum theory. | ||
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| 880 | 8 | |6 505-00/(S |a 5. Kinetic energy and Riemannian geometry6. 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 λ-method; 6. Non-holonomic auxiliary conditions; 7. The stationary value of a definite integral; 8. The fundamental processes of the calculus of variations | |
| 880 | 8 | |6 505-00/(S |a 9. The commutative properties of the δ-process10. 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 | |
| 880 | 8 | |6 505-00/(S |a 8. Gauss' principle of least restraintV. THE LAGRANGIAN EQUATIONS OF MOTION; 1. Hamilton's principle; 2. The Lagrangian equations of motion and their invariance relative to point transformations; 3. The energy theorem as a consequence of Hamilton's principle; 4. Kinosthenic or ignorable variables and their elimination; 5. The forceless mechanics of Hertz; 6. The time as kinosthenic variable; Jacobi's principle; the principle of least action; 7. Jacobi's principle and Riemannian geometry; 8. Auxiliary conditions; the physical significance of the Lagrangian λ-factor | |
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| 952 | f | f | |a Middle Tennessee State University |b Main |c James E. Walker Library |d Electronic Resources |t 0 |h Library of Congress classification |
