Introduction |
The variational approach to mechanics / 1: |
The procedure of Euler and Lagrange / 2: |
Hamilton's procedure / 3: |
The calculus of variations / 4: |
Comparison between the vectorial and the variational treatments of mechanics / 5: |
Mathematical evaluation of the variational principles / 6: |
Philosophical evaluation of the variational approach to mechanics / 7: |
The Basic Concepts of Analytical Mechanics / I: |
The Principal viewpoints of analytical mechanics |
Generalized coordinates |
The configuration space |
Mapping of the space on itself |
Kinetic energy and Riemannian geometry |
Holonomic and non-holonomic mechanical systems |
Work function and generalized force |
Scleronomic and rheonomic systems / 8: |
The law of the conservation of energy |
The Calculus of Variations / II: |
The general nature of extremum problems |
The stationary value of a function |
The second variation |
Stationary value versus extremum value |
Auxiliary conditions |
The Lagrangian lambda-method |
Non-holonomic auxiliary conditions |
The stationary value of a definite integral |
The fundamental processes of the calculus of variations |
The commutative properties of the delta-process / 9: |
The stationary value of a definite integral treated by the calculus of variations / 10: |
The Euler-Lagrange differential equations for n degrees of freedom / 11: |
Variation with auxiliary conditions / 12: |
Non-holonomic conditions / 13: |
Isoperimetric conditions / 14: |
The calculus of variations and boundary conditions / 15: |
The problem of the elastic bar |
The principle of virtual work / III: |
The principle of virtual work for reversible displacements |
The equilibrium of a rigid body |
Equivalence of two systems of forces |
Equilibrium problems with auxiliary conditions |
Physical interpretation of the Lagrangian multiplier method |
Fourier's inequality |
D'Alembert's principle / IV: |
The force of inertia |
The place of d'Alembert's principle in mechanics |
The conservation of energy as a consequence of d'Alembert's principle |
Apparent forces in an accelerated reference system |
Einstein's equivalence hypothesis |
Apparent forces in a rotating reference system |
Dynamics of a rigid body |
The motion of the centre of mass |
Euler's equations |
Gauss' principle of least restraint |
The Lagrangian equations of motion / V: |
Hamilton's principle |
The Lagrangian equations of motion and their invariance relative to point transformations |
The energy theorem as a consequence of Hamilton's principle |
Kinosthenic or ignorable variables and their elimination |
The forceless mechanics of Hertz |
The time as kinosthenic variable; Jacobi's principle; the principle of least action |
Jacobi's principle and Riemannian geometry |
Auxiliary conditions; the physical significance of the Lagrangian lambda-factor |
Non-holonomic auxiliary conditions and polygenic forces |
Small vibrations about a state of equilibrium |
The Canonical Equations of motion / VI: |
Legendre's dual transformation |
Legendre's transformation applied to the Lagrangian function |
Transformation of the Lagrangian equations of motion |
The canonical integral |
The phase space and the space fluid |
The energy theorem as a consequence of the canonical equations |
Liouville's theorem |
Integral invariants, Helmholtz' circulation theorem |
The elimination of ignorable variables |
The parametric form of the |
  Introduction |
The variational approach to mechanics / 1: |
The procedure of Euler and Lagrange / 2: |