Classical Mechanics: From Particles to Continua and Regularity to Chaos [Hardcover]

This well-rounded and self-contained treatment of classical mechanics strikes a balance between examples, concepts, phenomena and formalism. While addressed to graduate students and their teachers, the minimal prerequisites and ground covered should make it useful also to undergraduates and researchers. Starting with conceptual context, physical principles guide the development. Chapters are modular and the presentation is precise yet accessible, with numerous remarks, footnotes and problems enriching the learning experience. Essentials such as Galilean and Newtonian mechanics, the Kepler problem, Lagrangian and Hamiltonian mechanics, oscillations, rigid bodies and motion in noninertial frames lead up to discussions of canonical transformations, angle-action variables, Hamilton-Jacobi and linear stability theory. Bifurcations, nonlinear and chaotic dynamics as well as the wave, heat and fluid equations receive substantial coverage. Techniques from linear algebra, differential equations, manifolds, vector and tensor calculus, groups, Lie and Poisson algebras and symplectic and Riemannian geometry are gently introduced. A dynamical systems viewpoint pervades the presentation. A salient feature is that classical mechanics is viewed as part of the wider fabric of physics with connections to quantum, thermal, electromagnetic, optical and relativistic physics highlighted. Thus, this book will also be useful in allied areas and serve as a stepping stone for embarking on research.

Mechanical systems with one degree of freedom.- Keplers gravitational two-body problem.- Newtonian to Lagrangian and Hamiltonian mechanics.- Introduction to special relativistic mechanics.- Dynamics viewed as a vector
eld on state space.- Small oscillations for one degree of freedom.- Nonlinear oscillations: pendulum and anharmonic oscillator.- Rigid body mechanics.- Motion in noninertial frames of reference.- Canonical transformations.- Angle-action variables.- Hamiltlƒt