Classical MechanicsClassical Mechanics presents an updated treatment of the dynamics of particles and particle systems suitable for students preparing for advanced study of physics and closely related fields, such as astronomy and the applied engineering sciences. Compared to older books on this subject, the mathematical treatment has been updated for the study of more advanced topics in quantum mechanics, statistical mechanics, and nonlinear and orbital mechanics. The text begins with a review of the principles of classical Newtonian dynamics of particles and particle systems and proceeds to show how these principles are modified and extended by developments in the field. The text ends with the unification of space and time given by the Special Theory of Relativity. In addition, Hamiltonian dynamics and the concept of phase space are introduced early on. This allows integration of the concepts of chaos and other nonlinear effects into the main flow of the text. The role of symmetries and the underlying geometric structure of space-time is a key theme. In the latter chapters, the connection between classical and quantum mechanics is examined in some detail. |
Contents
Chapter 1 Review of Newtonian Particle Mechanics | 1 |
Chapter 2 Vector Spaces and Coordinate Systems | 57 |
Chapter 3 Lagrangian and Hamiltonian Dynamics | 105 |
Chapter 4 Hamiltons Principle | 147 |
Chapter 5 Central Force Motion | 183 |
Chapter 6 Small Oscillations | 231 |
Chapter 7 Rotational Geometry and Kinematics | 273 |
Chapter 8 Rigid Body Motion | 323 |
Chapter 10 HamiltonJacobi Theory | 415 |
Chapter 11 Special Relativity | 451 |
Chapter 12 Waves Particles and Fields | 509 |
Appendix A International System of Units and Conversion Factors | 545 |
Appendix B Physical Constants and Solar System Data | 553 |
Appendix C Geometric Algebras in N Dimensions | 557 |
References | 561 |
| 567 | |
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Common terms and phrases
action-angle angle angular momentum angular velocity axis basis body frame canonical transformations center of mass Christoffel symbols components conserved constant constraint conditions contravariant coordinate system covariant cyclic defined degrees of freedom denote density derivative differential equations displacement dynamics Earth eigenvalue electromagnetic element equations of motion Euclidean space Euler-Lagrange equations Euler’s example force four-momentum frequency function geometric algebra given gives gravitational field Hamilton’s equations Hamiltonian inertia inertial frame infinitesimal integral invariant Kepler kinetic energy Lagrangian linear Lorentz manifold matrix metric tensor momenta Newton normal modes notation orbit orthogonal transformation parameter particle pendulum phase space physical plane Poisson Brackets polar potential energy precession principal problem quantum mechanics radial relative relativistic rigid body rotation scalar shown in Figure solution solve spacetime spherical spin spin group stationary surface symmetry theorem time-dependent trajectory units variables variation vector