| Preface | p. ix |
| Lagrangian Mechanics | p. 1 |
| Preliminary Results | p. 2 |
| Introductory Notions | p. 2 |
| Differential Principles of Mechanics | p. 20 |
| Lagrange's Equations | p. 45 |
| Space of Configurations | p. 46 |
| Lagrange's Equations of Second Kind | p. 57 |
| Transformations. First Integrals | p. 65 |
| Other Problems Concerning Lagrange's Equations | p. 83 |
| New Forms of Lagrange's Equations | p. 83 |
| Applications | p. 98 |
| Hamiltonian Mechanics | p. 115 |
| Hamilton's Equations | p. 115 |
| General Results | p. 115 |
| Lagrange's Brackets. Poisson's Brackets | p. 138 |
| Applications | p. 151 |
| The Hamilton-Jacobi Method | p. 160 |
| General Results | p. 160 |
| Systems of Equations with Separate Variables | p. 172 |
| Applications | p. 191 |
| Variational Principles. Canonical Transformations | p. 213 |
| Variational Principles | p. 213 |
| Mathematical Preliminaries | p. 214 |
| The General Integral Principle | p. 225 |
| Hamilton's Principle | p. 231 |
| Maupertuis's Principle. Other Variational Principles | p. 242 |
| Continuous Mechanical Systems | p. 254 |
| Canonical Transformations | p. 265 |
| General Considerations. Conditions of Canonicity | p. 265 |
| Structure of Canonical Transformations. Properties | p. 289 |
| Symmetry Transformations. Noether's Theorem. Conservation Laws | p. 300 |
| Symmetry Transformations. Noether's Theorem | p. 301 |
| Lie Groups | p. 311 |
| Space-Time Symmetries. Conservation Laws | p. 319 |
| Other Considerations on Analytical Methods in Dynamics of Discrete Mechanical Systems | p. 335 |
| Integral Invariants. Ergodic Theorems | p. 335 |
| Integral Invariants of Order 2s | p. 335 |
| Invariants of First Order | p. 341 |
| Ergodic Theorems | p. 354 |
| Periodic Motions. Action-Angle Variables | p. 356 |
| Periodic Motions. Quasi-Periodic Motions | p. 356 |
| Action-Angle Variables | p. 361 |
| Adiabatic Invariance | p. 365 |
| Methods of Exterior Differential Calculus. Elements of Invariantive Mechanics | p. 368 |
| Methods of Exterior Differential Calculus | p. 368 |
| Elements of Invariantive Mechanics | p. 373 |
| Applications | p. 385 |
| Formalisms in the Dynamics of Mechanical Systems | p. 390 |
| Formalisms in Spaces with s + 1 Dimensions | p. 390 |
| Formalism in Spaces with 2s + 1 or with 2s + 2 Dimensions | p. 394 |
| Nations on the Inverse Problem of Mechanics and the Birkhoffian formalism | p. 397 |
| Control Systems | p. 402 |
| Control Systems | p. 402 |
| Optimal Trajectories | p. 407 |
| Dynamics of Non-holonomic Mechanical Systems | p. 411 |
| Kinematics of Non-holonomic Mechanical Systems | p. 411 |
| General Considerations | p. 411 |
| Conditions of Holonomy. Quasi-co-ordinates. Non-holonomic Spaces | p. 421 |
| Lagrange's Equations. Other Equations of Motion | p. 430 |
| Motion of a Rigid Solid on a Fixed Surface | p. 430 |
| Lagrange's Equations | p. 436 |
| Applications | p. 443 |
| Other Equations of Motion | p. 467 |
| Gibbs-Appell Equations | p. 478 |
| Gibbs-Appell Equations of Motion | p. 478 |
| Applications | p. 482 |
| Other Problems on the Dynamics of Non-Holonomic Mechanical Systems | p. 491 |
| Collisions | p. 491 |
| First Integrals of the Equations of Motion | p. 498 |
| Stability and Vibrations | p. 505 |
| Stability of Mechanical Systems | p. 505 |
| Stability of Equilibrium | p. 505 |
| Stability of Motion | p. 537 |
| Applications | p. 554 |
| Vibrations of Mechanical Systems | p. 566 |
| Small Free Oscillations About a Stable Position of Equilibrium | p. 566 |
| Small Forced Oscillations | p. 597 |
| Non-linear Vibrations | p. 606 |
| Applications | p. 612 |
| Dynamical Systems. Catastrophes and Chaos | p. 629 |
| Continuous and Discrete Dynamical Systems | p. 630 |
| Continuous Linear Dynamical Systems | p. 630 |
| Non-linear Differential Equations and Systems of Non-linear Differential Equations | p. 648 |
| Discrete Linear Dynamical Systems | p. 675 |
| Elements of the Theory of Catastrophes | p. 682 |
| Ramifications | p. 683 |
| Elementary Catastrophes | p. 689 |
| Periodic Solutions. Global Bifurcations | p. 697 |
| Periodic Solutions | p. 698 |
| Global Bifurcations | p. 707 |
| Fractals. Chaotic Motions | p. 712 |
| Fractals | p. 712 |
| Chaotic Motions | p. 723 |
| Bibliography | p. 739 |
| Subject Index | p. 759 |
| Name Index | p. 765 |
| Table of Contents provided by Ingram. All Rights Reserved. |
