Classical Mechanics: From Particles to Continua and Regularity to Chaos

Contents: Preface. 1. Mechanical systems with one degree of freedom. 2. Kepler’s gravitational two-body problem. 3. Newtonian to Lagrangian and Hamiltonian mechanics. 4. Introduction to special relativistic mechanics. 5. Dynamics viewed as a vector field on state space. 6. Small oscillations for one degree of freedom. 7. Nonlinear oscillations: pendulum and anharmonic oscillator. 8. Rigid body mechanics. 9. Motion in noninertial frames of reference. 10. Canonical transformations. 11. Angle-action variables. 12. Hamilton-Jacobi equation. 13. Normal modes of oscillation and linear stability. 14. Bifurcations: qualitative changes in dynamics. 15. From regular to chaotic motion. 16. Dynamics of continuous deformable media. 17. Vibrations of a stretched string and the wave equation. 18. Heat diffusion equation and Brownian motion. 19. Introduction to fluid mechanics. Supplementary reading. References. Index.

This textbook is a self-contained treatment of classical mechanics that emphasizes its wider connections to other branches of physics, such as quantum mechanics, thermal physics, electromagnetism, optics, etc. While the mechanics of Galileo and Newton to that of Lagrange and Hamilton along with their applications form the core of the text, many modern developments have also been included. Special attention has been paid to pedagogy; thus the chapters have numerous explanatory remarks and examples, and are supplemented with problems. The sections of the book are arranged in a modular fashion to increase accessibility. This new text, with minimal demand on prerequisites, is suited for beginning researchers as well as advanced undergraduates. At the same time, instructors and practicing physicists will find the treatment novel.

Govind Krishnaswami is a Professor of Physics at the Chennai Mathematical Institute, India, and is a recipient of the Apker Award and Marie Curie, EPSRC and Ramanujan Fellowships. His research in areas such as particle physics, nonlinear dynamics and fluid mechanics has often exploited ideas and tools from classical mechanics. He has taught a wide variety of subjects and is known for the clarity of his pedagogical articles in Resonance, a journal of science education.