The variational principles of mechanics

Bibliography & Index

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. I. The Basic Concepts of Analytical Mechanics1. The principal view points 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 theconservation of energy; 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 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.

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.