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|   Introduction | |
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| The variational approach to mechanics | |
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| The procedure of Euler and Lagrange | |
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| Hamilton's procedure | |
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| The calculus of variations | |
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| Comparison between the vectorial and the variational treatments of mechanics | |
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| Mathematical evaluation of the variational principles | |
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| Philosophical evaluation of the variational approach to mechanics | |
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| The Basic Concepts of Analytical Mechanics | |
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| The Principal viewpoints of analytical mechanics | |
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| Generalized coordinates | |
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| The configuration space | |
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| Mapping of the space on itself | |
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| Kinetic energy and Riemannian geometry | |
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| Holonomic and non-holonomic mechanical systems | |
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| Work function and generalized force | |
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| Scleronomic and rheonomic systems | |
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| The law of the conservation of energy | |
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| The Calculus of Variations | |
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| The general nature of extremum problems | |
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| The stationary value of a function | |
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| The second variation | |
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| Stationary value versus extremum value | |
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| Auxiliary conditions | |
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| The Lagrangian lambda-method | |
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| Non-holonomic auxiliary conditions | |
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| The stationary value of a definite integral | |
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| The fundamental processes of the calculus of variations | |
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| The commutative properties of the delta-process | |
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| The stationary value of a definite integral treated by the calculus of variations | |
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| The Euler-Lagrange differential equations for n degrees of freedom | |
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| Variation with auxiliary conditions | |
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| Non-holonomic conditions | |
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| Isoperimetric conditions | |
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| The calculus of variations and boundary conditions | |
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| The problem of the elastic bar | |
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| The principle of virtual work | |
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| The principle of virtual work for reversible displacements | |
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| The equilibrium of a rigid body | |
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| Equivalence of two systems of forces | |
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| Equilibrium problems with auxiliary conditions | |
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| Physical interpretation of the Lagrangian multiplier method | |
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| Fourier's inequality | |
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| D'Alembert's principle | |
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| The force of inertia | |
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| The place of d'Alembert's principle in mechanics | |
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| The conservation of energy as a consequence of d'Alembert's principle | |
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| Apparent forces in an accelerated reference system | |
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| Einstein's equivalence hypothesis | |
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| Apparent forces in a rotating reference system | |
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| Dynamics of a rigid body | |
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| The motion of the centre of mass | |
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| Dynamics of a rigid body | |
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| Euler's equations | |
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| Gauss' principle of least restraint | |
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| The Lagrangian equations of motion | |
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| Hamilton's principle | |
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| The Lagrangian equations of motion and their invariance relative to point transformations | |
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| The energy theorem as a consequence of Hamilton's principle | |
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| Kinosthenic or ignorable variables and their elimination | |
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| The forceless mechanics of Hertz | |
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| The time as kinosthenic variable; Jacobi's principle; the principle of least action | |
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| Jacobi's principle and Riemannian geometry | |
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| Auxiliary conditions; the physical significance of the Lagrangian lambda-factor | |
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| Non-holonomic auxiliary conditions and polygenic forces | |
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| Small vibrations about a state of equilibrium | |
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| The Canonical Equations of motion | |
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| Legendre's dual transformation | |
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| Legendre's transformation applied to the Lagrangian function | |
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| Transformation of the Lagrangian equations of motion | |
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| The canonical integral | |
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| The phase space and the space fluid | |
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| The energy theorem as a consequence of the canonical equations | |
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| Liouville's theorem | |
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| Integral invariants, Helmholtz' circulation theorem | |
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| The elimination of ignorable variables | |
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| The parametric form of the | |