Part I Newtonian Mechanics in Moving Coordinate Systems
1 Newton's Equations in a Rotating Coordinate System
1.1 Introduction of the Operator D
1.2 Formulation of Newton's Equation in the Rotating Coordinate System
1.3 Newton's Equations in Systems with Arbitrary Relative Motion
2 Free Fall on the Rotating Earth
2.1 Perturbation Calculation
2.2 Method of Successive Approximation
2.3 Exact Solution
3 Foucault's Pendulum
3.1 Solution of the Differential Equations
3.2 Discussion of the Solution

Part II Mechanics of Particle Systems
4 Degrees of Freedom
4.1 Degrees of Freedom of a Rigid Body
5 Center of Gravity
6 Mechanical Fundamental Quantities of Systems of Mass Points
6.1 Linear Momentum of the Many-Body System
6.2 Angular Momentum of the Many-Body System
6.3 Energy Law of the Many-Body System
6.4 Transformation to Center-of-Mass Coordinates
6.5 Transformation of the Kinetic Energy

Part III Vibrating Systems
7 Vibrations of Coupled Mass Points
7.1 The Vibrating Chain
8 The Vibrating String
8.1 Solution of the Wave Equation
8.2 Normal Vibrations
9 Fourier Series
10 The Vibrating Membrane
10.1 Derivation of the Differential Equation
10.2 Solution of the Differential Equation
10.3 Inclusion of the Boundary Conditions
10.4 Eigenfrequencies
10.5 Degeneracy
10.6 Nodal Lines
10.7 General Solution
10.8 Superposition of Node Line Figures
10.9 The Circular Membrane
10.10 Solution of Bessel's Differential Equation

Part IV Mechanics of Rigid Bodies
11 Rotation About a Fixed Axis
11.1 Moment of Inertia
11.2 The Physical Pendulum
12 Rotation About a Point
12.1 Tensor of Inertia
12.2 Kinetic Energy of a Rotating Rigid Body
12.3 The Principal Axes of Inertia
12.4 Existence and Orthogonality of the Principal Axes
12.5 Transformation of the Tensor of Inertia
12.6 Tensor of Inertia in the System of Principal Axes
12.7 Ellipsoid of Inertia
13 Theory of the Top
13.1 The Free Top
13.2 Geometrical Theory of the Top
13.3 Analytical Theory of the Free Top
13.4 The Heavy Symmetric Top: Elementary Considerations
13.5 Further Applications of the Top
13.6 The Euler Angles
13.7 Motion of the Heavy Symmetric Top

Part V Lagrange Equations
14 Generalized Coordinates
14.1 Quantities of Mechanics in Generalized Coordinates
15 D'Alembert Principle and Derivation of the Lagrange Equations
15.1 Virtual Displacements
16 Lagrange Equation for Nonholonomic Constraints
17 Special Problems
17.1 Velocity-Dependent Potentials
17.2 Nonconservative Forces and Dissipation Function (Friction Function:
17.3 Nonholonomic Systems and Lagrange Multipliers

Part VI Hamiltonian Theory
18 Hamilton's Equations
18.1 The Hamilton Principle
18.2 General Discussion of Variational Principles
18.3 Phase Space and Liouville's Theorem
18.4 The Principle of Stochastic Cooling
19 Canonical Transformations
20 Hamilton-Jacobi Theory
20.1 Visual Interpretation of the Action Function S
20.2 Transition to Quantum Mechanics
21 Extended Hamilton-Lagrange Formalism
21.1 Extended Set of Euler-Lagrange Equations
21.2 Extended Set of Canonical Equations
21.3 Extended Canonical Transformations
22 Extended Hamilton-Jacobi Equation

Part VII Nonlinear Dynamics
23 Dynamical Systems
23.1 Dissipative Systems: Contraction of the Phase-Space Volume . . .
23.2 Attractors
23.3 Equilibrium Solutions
23.4 Limit Cycles
24 Stability of Time-Dependent Paths
24.1 Periodic Solutions
24.2 Discretization and Poincar6 Cuts
25 Bifurcations
25.1 Static Bifurcations
25.2 Bifurcations of Time-Dependent Solutions
26 Lyapunov Exponents and Chaos
26.1 One-Dimensional Systems
26.2 Multidimensional Systems
26.3 Stretching and Folding in Phase Space
26.4 Fractal Geometry
27 Systems with Chaotic Dynamics
27.1 Dynamics of Discrete Systems
27.2 One-Dimensional Mappings

Part VIII On the History of Mechanics
28 Emergence of Occidental Physics in the Seventeenth Century Notes
Recommendations for Further Reading on Theoretical Mechanics
Index