| | | [frontespizio] |
| | | [colophon] |
| 0.01 | | [dedica] |
| 0.03 | | Contents |
| 43489;1980.01 | 0.07 | | Preface to Second Edition [ di Herbert Goldstein ] |
| 19138;1950.03 | 0.11 | | Preface to the First Edition [ di Herbert Goldstein ] |
| 0.14 | | __ |
| 0.14 | | ____ |
| | | {testo} |
| 1 | Chapter 1. | Survey of the Elementary Principles |
| 1 | 1-1 | Mechanics of a particle |
| 5 | 1-2 | Mechanics of a system of particles |
| 11 | 1-3 | Contraints |
| 17 | 1-4 | D'Alembert's principle and Lagrange's equations |
| 21 | 1-5 | Velocity-dependent potentials and the dissipation function |
| 25 | 1-6 | Simple applications of the Lagrangian formulation |
| 35 | Chapter 2. | Variational Principles and Lagrange's Equations |
| 35 | 2-1 | Hamilton's principle |
| 37 | 2-2 | Some techiques of the calculus of variations |
| 43 | 2-3 | Derivation of Lagrange's equations from Hamilton's principle |
| 45 | 2-4 | Extension of Hamilton's principle to nonholonomic systems |
| 51 | 2-5 | Advantages of a variational principle formulation |
| 54 | 2-6 | Conservation theorems and symmetry properties |
| 70 | Chapter 3. | The Two-Body Central Force Problem |
| 70 | 3-1 | reduction to the equivalent one-body problem |
| 71 | 3-2 | The equations of motion and first integrals |
| 77 | 3-3 | The equivalent one-dimensioal problem, and classification of orbits |
| 82 | 3-4 | The virial theorem |
| 85 | 3-5 | The differential equation for the orbit, and integrable power-law potentials |
| 90 | 3-6 | Conditions for closed orbits (Bertrand's theorem) |
| 94 | 3-7 | The Kepler problem: Inverse square law of force |
| 98 | 3-8 | The motion in time in the Kepler problem |
| 102 | 3-9 | The Laplace-Runge-Lenz vector |
| 105 | 3-10 | Scattering in a central force field |
| 114 | 3-11 | Trasformation of the scattering problem to laboratory coordiates |
| 128 | Chapter 4. | The Kinematics of Rigid Body Motion |
| 128 | 4-1 | The independent coordinates of a rigid body |
| 132 | 4-2 | Orthogonal transforrmations |
| 137 | 4-3 | Formal properties of the trasformation matrix |
| 143 | 4-4 | The Euler angles |
| 148 | 4-5 | The Cayley-Klein parameters and related quantities |
| 158 | 4-6 | Euler's theorem on the motion of a rigid body |
| 164 | 4-7 | Finite rotations |
| 166 | 4-8 | Infinitesimal rotations |
| 174 | 4-9 | Rate of change of a vector |
| 177 | 4-10 | The Coriolis force |
| 188 | Chapter 5. | The Rigid Body Equations of Motion |
| 188 | 5-1 | Angular momentum and kinetic energy of motion about a point |
| 192 | 5-2 | Tensors and dyadics |
| 195 | 5-3 | The inertia tensor and the moment of inertia |
| 198 | 5-4 | The eigenvalues of the inertia tensor and the principal axis transformation |
| 203 | 5-5 | Methods of solving rigid body problems and the Euler equations of motion |
| 205 | 5-6 | Torque-free motion of a rigid body |
| 213 | 5-7 | The neavy symmetrical top with one point fixed |
| 225 | 5-8 | Precession of the equinoxes and the satellite orbits |
| 232 | 5-9 | Precession of systems of charges in a magetic field |
| 243 | Chapter 6. | Small Oscillations |
| 243 | 6-1 | Formulation of the Problem |
| 246 | 6-2 | The eingenvalue equation ad the principal axis transformation |
| 253 | 6-3 | Frequencies of free vibration, anf normal coordinates |
| 258 | 6-4 | Free vibrations of a linear triatomic molecule |
| 263 | 6-5 | Forced vibrations and the effect of dissipative forces |
| 275 | Chapter 7. | Special Relativity in Classical Mechanics |
| 275 | 7-1 | The basic program of special relativity |
| 278 | 7-2 | The Lorentz transformation |
| 288 | 7-3 | Lorentz transformations in real four dimensional spaces |
| 293 | 7-4 | Further descriptions of the Lorentz transformation |
| 298 | 7-5 | Covariant four-dimensional formulations |
| 303 | 7-6 | The force and energy equations in relativistic mechanics |
| 309 | 7-7 | Relativistic kinematics of collisions and many-particle systems |
| 320 | 7-8 | The Lagrangian formulation of relativistic mechanics |
| 326 | 7-9 | Covariant Lagragian formulations |
| 339 | Chapter 8. | The Hamilton Equations of Motion |
| 339 | 8-1 | Legendre transformations and the Hamilton equations of motion |
| 347 | 8-2 | Cyclic coordinates and conservation theorems |
| 351 | 8-3 | Routh's procedure and oscillations about steady motion |
| 356 | 8-4 | The Hamiltonian formulation of relativistic mechanics |
| 362 | 8-5 | Derivation of Hamilton's equations from variational principle |
| 365 | 8-6 | The principle of least action |
| 378 | Chapter 9. | Canonical Transformations |
| 378 | 9-1 | The equations of canonical transformation |
| 386 | 9-2 | Examples of canoical transformatons |
| 391 | 9-3 | The symplectic approch to canocnical transformations |
| 397 | 9-4 | Poisson brackets and other canonical invariants |
| 405 | 9-5 | Equations of motion, infinitesimal canonical transformations, and conservation theorems in the Poisso bracket formulation |
| 420 | 9-7 | Simmetry groups of mechanical systems |
| 416 | 9-6 | The angular momentum Poisson bracket relations |
| 426 | 9-8 | Liouville's theorem |
| 438 | Chapter 10. | Hamilton-Jacobi Theory |
| 438 | 10-1 | The Hamilton-Jacobi equation for Hamilton's principal function |
| 442 | 10-2 | The harmonic oscillator problem as an example of the Hamilton-Jacobi method |
| 445 | 10-3 | The Hamilton-Jacobi equation for Hamilton's characteristic function |
| 449 | 10-4 | Separation of variables in the Hamilton-Jacobi equation |
| 457 | 10-5 | Action-angle variables i systems of one degree of freedom |
| 463 | 10-6 | Action-angle variables for completely separable systems |
| 472 | 10-7 | The Kepler problem in action-angle variables |
| 484 | 10-8 | Hamilton-Jacobi theory, geometrical optics, and wave mechanics |
| 499 | Chapter 11. | Canonical Perturbation Theory |
| 499 | 11-1 | Introduction |
| 500 | 11-2 | Time-dependent perturbation (variation of constants) |
| 506 | 11-3 | Illustrations of time-dependent perturbation theory |
| 515 | 11-4 | Time-dependent perturbation theory in first order with one degree of freedom |
| 519 | 11-5 | Time-independent perturbation theory to higher order |
| 527 | 11-6 | Specialized perturbartion techniques in celestial and space mechanics |
| 531 | 11-7 | adiabatic invariants |
| 545 | Chapter 12. | Introduction to the Lagrangian and Hamiltonian Formualtions for Continuos Systems and Fields |
| 545 | 12-1 | The transition from a discret to a continuos system |
| 548 | 12-2 | The Lagrangian formulation for continuous systems |
| 555 | 12-3 | The stress-energy tensor and conservation theorems |
| 562 | 12-4 | Hamiltonian formulation, Poisson brackets and the momentum represetation |
| 570 | 12-5 | Relativistic field theory |
| 575 | 12-6 | Examples of relativistic field theories |
| 588 | 12-7 | Noether's theorem |
| 601 | | Appendixes |
| 601 | A | Proof of Bertrand's Theorem |
| 606 | B | Euler Angles in Alternate Conventions |
| 611 | C | Transformation Properties of dΩ |
| 613 | D | The Staeckel Conditions for Separability of the Hamilton-Jacobi Equation |
| 616 | E | Lagrangian Formulation of the Acoustic Field in Gases |
| 621 | | Bibliography |
| 631 | | Index of Symbols |
| 643 | | Index |
| 672 | | _ |
| 672 | | ___ |
