| 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： |
図書
