Classical Mechanics Systems of Particles and Hamiltonian Dynamics

This textbook Classical Mechanics provides a complete survey on all aspects of classical mechanics in theoretical physics. An enormous number of worked examples and problems show students how to apply the abstract principles to realistic problems.

The textbook covers Newtonian mechanics in rotating coordinate systems, mechanics of systems of point particles, vibrating systems and mechanics of rigid bodies. It thoroughly introduces and explains the Lagrange and Hamilton equations and the Hamilton-Jacobi theory. A large section on nonlinear dynamics and chaotic behavior of systems takes Classical Mechanics to newest development in physics.

The new edition is completely revised and updated. New exercises and new sections in canonical transformation and Hamiltonian theory have been added.

Newtonian Mechanics in Moving Coordinate Systems.- Newton’s Equations in a Rotating Coordinate System.- Free Fall on the Rotating Earth.- Foucault’s Pendulum.- Mechanics of Particle Systems.- Degrees of Freedom.- Center of Gravity.- Mechanical Fundamental Quantities of Systems of Mass Points.- Vibrating Systems.- Vibrations of Coupled Mass Points.- The Vibrating String.- Fourier Series.- The Vibrating Membrane.- Mechanics of Rigid Bodies.- Rotation About a Fixed Axis.- Rotation About a Point.- Theory of the Top.- Lagrange Equations.- Generalized Coordinates.- D’Alembert Principle and Derivation of the Lagrange Equations.- Lagrange Equation for Nonholonomic Constraints.- Special Problems.- Hamiltonian Theory.- Hamilton’s Equations.- Canonical Transformations.- Hamilton–Jacobi Theory.- Extended Hamilton–Lagrange Formalism.- Extended Hamilton–Jacobi Equation.- Nonlinear Dynamics.- Dynamical Systems.- Stability of Time-Dependent Paths.- Bifurcations.- Lyapunov Exponents and Chaos.- Systemswith Chaotic Dynamics.- On the History of Mechanics.- Emergence of Occidental Physics in the Seventeenth Century.