THE VARIATIONAL PRINCIPLES OF MECHANICS LANCZOS PDF

The variational approach to mechanics 2. The procedure of Euler and Lagrange 3. 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.

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The variational approach to mechanics 2. The procedure of Euler and Lagrange 3. 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 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 The stationary value of a definite integral treated by the calculus of variations The Euler-Lagrange differential equations for n degrees of freedom Variation with auxiliary conditions Non-holonomic conditions 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. The force of inertia 2.

Apparent forces in an accelerated reference system. Apparent forces in a rotating reference system 6. Dynamics of a rigid body.

The motion of the centre of mass 7. The Lagrangian equations of motion 1. The Lagrangian equations of motion and their invariance relative to point transformations 3. Kinosthenic or ignorable variables and their elimination 5.

The forceless mechanics of Hertz 6. Auxiliary conditions; the physical significance of the Lagrangian lambda-factor 9. Non-holonomic auxiliary conditions and polygenic forces Small vibrations about a state of equilibrium VI. The Canonical Equations of motion 1. 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. The elimination of ignorable variables 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. 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. The Partial differential equation of Hamilton-Jacobi 1. The importance of the generating function for the problem of motion 2. Solution of the partial differential equation by separation 4.

The role of the partial differential equation in the theories of Hamilton and Jacobi 6. Geometrical solution of the partial differential equation. The geometrization of dynamics. Non-Riemannian geometrics. Relativistic Mechanics.

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