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|Additional Physical Format:||Print version:
Lanczos, Cornelius, 1893-1974.
Variational principles of mechanics.
|Material Type:||Document, Internet resource|
|Document Type:||Internet Resource, Computer File|
|All Authors / Contributors:||
|Notes:||Reprint. Originally published: Toronto : University of Toronto Press, ©1970. (Mathematical expositions ; no. 4).|
|Description:||1 online resource (xxix, 418 pages) : illustrations.|
|Contents:||Cover Page; Title Page; Copyright Page; Dedication; Preface; Preface to the Second Edition; Preface to the Second Edition; Preface to the Second Edition; Contents; 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 approachto mechanics; The Variational Principles of Mechanics. 6. Non-holonomic auxiliary conditions7. The stationary value of a definite integral; 8. The fundamental processes of the calculus of variations; 9. The commutative properties of the 5-process; 10. The stationary value of a definite integral treated by the calculus of variations; 11. The Euler-Lagrange differential equations for n degreesof 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; II. The Calculus of Variations. 1. The principle of virtual work for reversible displacements2. 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. Fourier's inequality; III. The Principle of Virtual Work; 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 system6. Dynamics of a rigid body. The motion of the centre of mass; 7. Dynamics of a rigid body. Euler's equations; 8. Gauss' principle of least restraint; IV. D'alembert's Principle; 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'sprinciple; 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.|
|Series Title:||Dover books on physics and chemistry.; Mathematical expositions, no. 4.|
|Responsibility:||by Cornelius Lanczos.|