This volume of lectures, Classical Mechanics: Systems of Particles and Hamiltonian Dynamics, deals with the second and more advanced part of the important field of classical mechanics. We have tried to present the subject in a manner that is both interesting to the student and easily accessible. The main text is therefore accompanied by many exercises and examples that have been worked out in great detail. This should make the book useful also for students wishing to study the subject on their own.

Foreword

Preface

Examples

Ⅰ NEWTONIAN MECHANICS IN MOVING COORDINATE SYSTEMS

 1 Newton's Equations in a Rotating Coordinate System

Introduction of the operator

Formulation of Newton's equation in the rotating coordinate system

Newton's equations in systems with arbitrary relative motion

 2 Free Fall on the Rotating Earth

Perturbation calculation

Method of successive approximation

Exact solution

 3 Foucault's Pendulum

Solution of the differential equations

Discussion of the solution

Ⅱ MECHANICS OF PARTICLE SYSTEMS

 4 Degrees of Freedom

Degrees of freedom of a rigid body

 5 Center of Gravity

 6 Mechanical Fundamental Quantities of Systems of Mass Points

Linear momentum of the many-body system

Angular momentum of the many-body system

Energy law of the many-body system

Transformation to center-of-mass coordinates

Transformation of the kinetic energy

Ⅲ VIBRATING SYSTEMS

 7 Vibrations of Coupled Mass Points

The vibrating chain

 8 The Vibrating String

Solution of the wave equation

Normal vibrations

 9 Fourier Series

10 The Vibrating Membrane

Derivation of the differential equation

Solution of the differential equation: Rectangular membrane

Inclusion of the boundary conditions

Eigenfrequencies

Degeneracy

Nodal lines

General solution (inclusion of the initial conditions)

Superposition of node line figures

The circular membrane

Solution of Bessel's differential equation

Ⅳ  MECHANICS OF RIGID BODIES

 11 Rotation About a Fixed Axis

Moment of inertia (elementary consideration)

The physical pendulum

 12 Rotation About a Point

Tensor of inertia

Kinetic energy of a rotating rigid body

The principal axes of inertia

Existence and orthogonality of the principal axes

Transformation of the tensor of inertia

Tensor of inertia in the system of principal axes

Ellipsoid of inertia

 13 Theory of the Top

The free top

Geometrical theory of the top

Analytical theory of the free top

The heavy symmetric top: Elementary considerations

Further applications of the top

The Euler angles

Motion of the heavy symmetric top

Ⅴ  LAGRANGE EQUATIONS

 14 Generalized Coordinates

Quantities of mechanics in generalized coordinates

 15 D'Alembert Principle and Derivation of the Lagrange Equations

Virtual displacements

 16 Lagrange Equation for Nonholonomic Constraints

 17 Special Problems

Velocity-dependent potentials

Nonconservative forces and dissipation function (friction function)

Nonholonomic systems and Lagrange multipliers

Ⅵ HAMILTONIAN THEORY

 18 Hamilton's Equations

The Hamilton principle

General discussion of variational principles

Phase space and Liouville's theorem

The principle of stochastic cooling

 19 Canonical Transformations

 20 Hamilton-Jacobi Theory

Visual interpretation of the action function S

Transition to quantum mechanics

Ⅶ NONLINEAR DYNAMICS

 21 Dynamical Systems

Dissipative systems: Contraction of the phase-space volume

Attractors

Equilibrium solutions

Limit cycles

 22 Stability of Time-Dependent Paths

Periodic solutions

Discretization and Poincare cuts

 23 Bifurcations

Static bifurcations

Bifurcations of time-dependent solutions

 24 Lyapunov Exponents and Chaos

One-dimensional systems

Multidimensional systems

Stretching and folding in phase space

Fractal geometry

 25 Systems with Chaotic Dynamics

Dynamics of discrete systems

One-dimensional mappings

Ⅷ  ON THE HISTORY OF MECHANICS

 26 Emergence of Occidental Physics in the Seventeenth Century

Notes

Recommendations for further reading on theoretical mechanics

Index