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
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