Table of Contents
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Table of Contents
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Licensing
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Preface
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Prologue
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1: A brief History of Classical Mechanics
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2: Review of Newtonian Mechanics
- 2.1: Introduction to Newtonian Mechanics
- 2.2: Newton's Laws of motion
- 2.3: Inertial Frames of reference
- 2.4: First-order Integrals in Newtonian mechanics
- 2.5: Conservation Laws in Classical Mechanics
- 2.6: Motion of finite-sized and many-body systems
- 2.7: Center of Mass of a Many-Body System
- 2.8: Total Linear Momentum of a Many-body System
- 2.9: Angular Momentum of a Many-Body System
- 2.10: Work and Kinetic Energy for a Many-Body System
- 2.11: Virial Theorem
- 2.12: Applications of Newton's Equations of Motion
- 2.13: Solution of many-body equations of motion
- 2.14: Newton's Law of Gravitation
- 2.E: Review of Newtonian Mechanics (Exercises)
- 2.S: Newtonian Mechanics (Summary)
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3: Linear Oscillators
- 3.1: Introduction to Linear Oscillators
- 3.2: Linear Restoring Forces
- 3.3: Linearity and Superposition
- 3.4: Geometrical Representations of Dynamical Motion
- 3.5: Linearly-damped Free Linear Oscillator
- 3.6: Sinusoidally-driven, linearly-damped, linear oscillator
- 3.7: Wave equation
- 3.8: Travelling and standing wave solutions of the wave equation
- 3.9: Waveform Analysis
- 3.10: Signal Processing
- 3.11: Wave Propagation
- 3.E: Linear Oscillators (Exercises)
- 3.S: Linear Oscillators (Summary)
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4: Nonlinear Systems and Chaos
- 4.1: Introduction to Nonlinear Systems and Chaos
- 4.2: Weak Nonlinearity
- 4.3: Bifurcation and Point Attractors
- 4.4: Limit Cycles
- 4.5: Harmonically-driven, linearly-damped, plane pendulum
- 4.6: Differentiation Between Ordered and Chaotic Motion
- 4.7: Wave Propagation for Non-linear Systems
- 4.E: Nonlinear Systems and Chaos (Exercises)
- 4.S: Nonlinear Systems and Chaos (Summary)
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5: Calculus of Variations
- 5.1: Introduction to the Calculus of Variations
- 5.2: Euler’s Differential Equation
- 5.3: Applications of Euler’s Equation
- 5.4: Selection of the Independent Variable
- 5.5: Functions with Several Independent Variables
- 5.6: Euler’s Integral Equation
- 5.7: Constrained Variational Systems
- 5.8: Generalized coordinates in Variational Calculus
- 5.9: Lagrange multipliers for Holonomic Constraints
- 5.10: Geodesic
- 5.11: Variational Approach to Classical Mechanics
- 5.E: Calculus of Variations (Exercises)
- 5.S: Calculus of Variations (Summary)
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6: Lagrangian Dynamics
- 6.1: Introduction to Lagrangian Dynamics
- 6.2: Newtonian plausibility argument for Lagrangian mechanics
- 6.3: Lagrange Equations from d’Alembert’s Principle
- 6.4: Lagrange equations from Hamilton’s Principle
- 6.5: Constrained Systems
- 6.6: Applying the Euler-Lagrange equations to classical mechanics
- 6.7: Applications to unconstrained systems
- 6.8: Applications to systems involving holonomic constraints
- 6.9: Applications involving Non-holonomic Constraints
- 6.10: Velocity-dependent Lorentz force
- 6.11: Time-dependent forces
- 6.12: Impulsive Forces
- 6.13: The Lagrangian versus the Newtonian approach to classical mechanics
- 6.E: Lagrangian Dynamics (Exercises)
- 6.S: Lagrangian Dynamics (Summary)
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7: Symmetries, Invariance and the Hamiltonian
- 7.1: Introduction to Symmetries, Invariance, and the Hamiltonian
- 7.2: Generalized Momentum
- 7.3: Invariant Transformations and Noether’s Theorem
- 7.4: Rotational invariance and conservation of angular momentum
- 7.5: Cyclic Coordinates
- 7.6: Kinetic Energy in Generalized Coordinates
- 7.7: Generalized Energy and the Hamiltonian Function
- 7.8: Generalized energy theorem
- 7.9: Generalized energy and total energy
- 7.10: Hamiltonian Invariance
- 7.11: Hamiltonian for Cyclic Coordinates
- 7.12: Symmetries and Invariance
- 7.13: Hamiltonian in Classical Mechanics
- 7.E: Symmetries, Invariance and the Hamiltonian (Exercises)
- 7.S: Symmetries, Invariance and the Hamiltonian (Summary)
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8: Hamiltonian Mechanics
- 8.1: Introduction
- 8.2: Legendre Transformation between Lagrangian and Hamiltonian mechanics
- 8.3: Hamilton’s Equations of Motion
- 8.4: Hamiltonian in Different Coordinate Systems
- 8.5: Applications of Hamiltonian Dynamics
- 8.6: Routhian Reduction
- 8.7: Variable-mass systems
- 8.E: Hamiltonian Mechanics (Exercises)
- 8.S: Hamiltonian Mechanics (Summary)
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9: Hamilton's Action Principle
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10: Nonconservative Systems
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11: Conservative two-body Central Forces
- 11.1: Introduction to Conservative two-body Central Forces
- 11.2: Equivalent one-body Representation for two-body motion
- 11.3: Angular Momentum
- 11.4: Equations of Motion
- 11.5: Differential Orbit Equation
- 11.6: Hamiltonian
- 11.7: General Features of the Orbit Solutions
- 11.8: Inverse-square, two-body, central force
- 11.9: Isotropic, linear, two-body, central force
- 11.10: Closed-orbit Stability
- 11.11: The Three-Body Problem
- 11.12: Two-body Scattering
- 11.13: Two-body kinematics
- 11.E: Conservative two-body Central Forces (Exercises)
- 11.S: Conservative two-body Central Forces (Summary)
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12: Non-inertial Reference Frames
- 12.1: Introduction to Non-inertial Reference Frames
- 12.2: Translational acceleration of a reference frame
- 12.3: Rotating Reference Frame
- 12.4: Reference Frame Undergoing Rotation Plus Translation
- 12.5: Newton’s Law of Motion in a Non-Inertial Frame
- 12.6: Lagrangian Mechanics in a Non-Inertial Frame
- 12.7: Centrifugal Force
- 12.8: Coriolis Force
- 12.9: Routhian Reduction for Rotating Systems
- 12.10: Effective gravitational force near the surface of the Earth
- 12.11: Free Motion on the Earth
- 12.12: Weather systems
- 12.13: Foucault pendulum
- 12.E: Non-inertial reference frames (Exercises)
- 12.S: Non-inertial reference frames (Summary)
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13: Rigid-body Rotation
- 13.1: Introduction to Rigid-body Rotation
- 13.2: Rigid-body Coordinates
- 13.3: Rigid-body Rotation about a Body-Fixed Point
- 13.4: Inertia Tensor
- 13.5: Matrix and Tensor Formulations of Rigid-Body Rotation
- 13.6: Principal Axis System
- 13.7: Diagonalize the Inertia Tensor
- 13.8: Parallel-Axis Theorem
- 13.9: Perpendicular-axis Theorem for Plane Laminae
- 13.10: General Properties of the Inertia Tensor
- 13.11: Angular Momentum and Angular Velocity Vectors
- 13.12: Kinetic Energy of Rotating Rigid Body
- 13.13: Euler Angles
- 13.14: Angular Velocity
- 13.15: Kinetic energy in terms of Euler angular velocities
- 13.16: Rotational Invariants
- 13.17: Euler’s equations of motion for rigid-body rotation
- 13.18: Lagrange equations of motion for rigid-body rotation
- 13.19: Hamiltonian equations of motion for rigid-body rotation
- 13.20: Torque-free rotation of an inertially-symmetric rigid rotor
- 13.21: Torque-free rotation of an asymmetric rigid rotor
- 13.22: Stability of torque-free rotation of an asymmetric body
- 13.23: Symmetric rigid rotor subject to torque about a fixed point
- 13.24: The Rolling Wheel
- 13.25: Dynamic balancing of wheels
- 13.26: Rotation of Deformable Bodies
- 13.E: Rigid-body Rotation (Exercises)
- 13.S: Rigid-body Rotation (Summary)
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14: Coupled Linear Oscillators
- 14.1: Introduction to Coupled Linear Oscillators
- 14.2: Two Coupled Linear Oscillators
- 14.3: Normal Modes
- 14.4: Center of Mass Oscillations
- 14.5: Weak Coupling
- 14.6: General Analytic Theory for Coupled Linear Oscillators
- 14.7: Two-body coupled oscillator systems
- 14.8: Three-body coupled linear oscillator systems
- 14.9: Molecular coupled oscillator systems
- 14.10: Discrete Lattice Chain
- 14.11: Damped Coupled Linear Oscillators
- 14.12: Collective Synchronization of Coupled Oscillators
- 14.E: Coupled linear oscillators (Exercises)
- 14.S: Coupled linear oscillators (Summary)
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15: Advanced Hamiltonian Mechanics
- 15.1: Introduction to Advanced Hamiltonian Mechanics
- 15.2: Poisson bracket Representation of Hamiltonian Mechanics
- 15.3: Canonical Transformations in Hamiltonian Mechanics
- 15.4: Hamilton-Jacobi Theory
- 15.5: Action-angle Variables
- 15.6: Canonical Perturbation Theory
- 15.7: Symplectic Representation
- 15.8: Comparison of the Lagrangian and Hamiltonian Formulations
- 15.E: Advanced Hamiltonian Mechanics (Exercises)
- 15.S: Advanced Hamiltonian mechanics (Summary)
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16: Analytical Formulations for Continuous Systems
- 16.1: Introduction
- 16.2: The Continuous Uniform Linear Chain
- 16.3: The Lagrangian density formulation for continuous systems
- 16.4: The Hamiltonian density formulation for continuous systems
- 16.5: Linear Elastic Solids
- 16.6: Electromagnetic Field Theory
- 16.7: Ideal Fluid Dynamics
- 16.8: Viscous Fluid Dynamics
- 16.9: Summary and Implications
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17: Relativistic Mechanics
- 17.1: Introduction to Relativistic Mechanics
- 17.2: Galilean Invariance
- 17.3: Special Theory of Relativity
- 17.4: Relativistic Kinematics
- 17.5: Geometry of Space-time
- 17.6: Lorentz-Invariant Formulation of Lagrangian Mechanics
- 17.7: Lorentz-invariant formulations of Hamiltonian Mechanics
- 17.8: The General Theory of Relativity
- 17.9: Implications of Relativistic Theory to Classical Mechanics
- 17.E: Relativistic Mechanics (Exercises)
- 17.S: Relativistic Mechanics (Summary)
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18: The Transition to Quantum Physics
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19: Mathematical Methods for Classical Mechanics
- 19.1: Introduction
- 19.2: Appendix - Matrix Algebra
- 19.3: Appendix - Vector algebra
- 19.4: Appendix - Orthogonal Coordinate Systems
- 19.5: Appendix - Coordinate transformations
- 19.6: Appendix - Tensor Algebra
- 19.7: Appendix - Aspects of Multivariate Calculus
- 19.8: Appendix - Vector Differential Calculus
- 19.9: Appendix - Vector Integral Calculus
- 19.10: Appendix - Waveform analysis
- 19.11: Bibliography
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Epilogue
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Index
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Glossary
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Detailed Licensing