Classical mechanics

Description

Content: Kinematics: Describing the Motion Introduction Space, Time, and Coordinate Systems Change of Coordinate System (Transformation of Components of a Vector) Displacement Vector Speed and Velocity Acceleration Velocity and Acceleration in Polar Coordinates Angular Velocity and Angular Acceleration Infinitesimal Rotations and the Angular Velocity Vector Newtonian Mechanics The First Law of Motion (Law of Inertia) The Second Law of Motion the Equations of Motion The Third Law of Motion Galilean Transformations and Galilean Invariance Newton's Laws of Rotational Motion Work, Energy, and Conservation Laws Systems of Particles References Integration of Newton's Equation of Motion Introduction Motion Under Constant Force Force Is a Function of Time Force Is a Function of Velocity Force Is a Function of Position Time-Varying Mass System (Rocket System) Lagrangian Formulation of Mechanics: Descriptions of Motion in Configuration Space Generalized Coordinates and Constraints Kinetic Energy in Generalized Coordinates Generalized Momentum Lagrangian Equations of Motion Nonuniqueness of the Lagrangian Integrals of Motion and Conservation Laws Scale Invariance Nonconservative Systems and Generalized Potential Charged Particle in Electromagnetic Field Forces of Constraint and Lagrange's Multipliers Lagrangian versus Newtonian Approach to Classical Mechanics Reference Hamiltonian Formulation of Mechanics: Descriptions of Motion in PhaseSpaces The Hamiltonian of a Dynamic System Hamilton's Equations of Motion Integrals of Motion and Conservation Theorems Canonical Transformations Poisson Brackets Poisson Brackets and Quantum Mechanics Phase Space and Liouville's Theorem Time Reversal in Mechanics (Optional) Passage from Hamiltonian to Lagrangian References Motion Under a Central Force Two-Body Problem and Reduced Mass General Properties of Central Force Motion Effective Potential and Classification of Orbits General Solutions of Central Force Problem Inverse Square Law of Force Kepler's Three Laws of Planetary Motion Applications of Central Force Motion Newton's Law of Gravity from Kepler's Laws Stability of Circular Orbits (Optional) Apsides and Advance of Perihelion (Optional) Laplace-Runge-Lenz Vector and the Kepler Orbit (Optional) References Harmonic Oscillator Simple Harmonic Oscillator Adiabatic Invariants and Quantum Condition Damped Harmonic Oscillator Phase Diagram for Damped Oscillator Relaxation Time Phenomena Forced Oscillations without Damping Forced Oscillations with Damping Oscillator Under Arbitrary Periodic Force Vibration Isolation Parametric Excitation Coupled Oscillations and Normal Coordinates Coupled Pendulum Coupled Oscillators and Normal Modes: General Analytic Approach Forced Oscillations of Coupled Oscillators Coupled Electric Circuits Nonlinear Oscillations Qualitative Analysis: Energy and Phase Diagrams Elliptical Integrals and Nonlinear Oscillations Fourier Series Expansions The Method of Perturbation Ritz Method Method of Successive Approximation Multiple Solutions and Jumps Chaotic Oscillations References Collisions and Scatterings Direct Impact of Two Particles Scattering Cross Sections and Rutherford Scattering Laboratory and Center-of-Mass Frames of Reference Nuclear Sizes Small-Angle Scattering (Optional) References Motion in Non-Inertial Systems Accelerated Translational Coordinate System Dynamics in Rotating Coordinate System Motion of Particle Near the Surface of the Earth Foucault Pendulum Larmor's Theorem Classical Zeeman Effect Principle of Equivalence Motion of Rigid Bodies Independent Coordinates of Rigid Body Eulerian Angles Rate of Change of Vector Rotational Kinetic Energy and Angular Momentum Inertia Tensor Euler's Equations of Motion Motion of a Torque-Free Symmetrical Top Motion of Heavy Symmetrical Top with One Point Fixed Stability of Rotational Motion References Theory of Special Relativity Historical Origin of Special Theory of Relativity Michelson-Morley Experiment Postulates of Special Theory of Relativity Lorentz Transformations Doppler Effect Relativistic Space-Time (Minkowski Space) Equivalence of Mass and Energy Conservation Laws of Energy and Momentum Generalization of Newton's Equation of Motion Relativistic Lagrangian and Hamiltonian Functions Relativistic Kinematics of Collisions Collision Threshold Energies References Newtonian Gravity and Newtonian Cosmology Newton's Law of Gravity Gravitational Field and Gravitational Potential Gravitational Field Equations: Poisson's and Laplace's Equations Gravitational Field and Potential of Extended Body Tides General Theory of Relativity: Relativistic Theory of Gravitation Introduction to Cosmology Brief History of Cosmological Ideas Discovery of Expansion of the Universe, Hubble's Law Big Bang Formulating Dynamical Models of the Universe Cosmological Red Shift and Hubble Constant H Critical Mass Density and Future of the Universe Microwave Background Radiation Dark Matter Reference Hamilton-Jacobi Theory of Dynamics Canonical Transformation and H-J Equation Action and Angle Variables Infinitesimal Canonical Transformations and Time Development Operator H-J Theory and Wave Mechanics Reference Introduction to Lagrangian and Hamiltonian Formulations for Continuous Systems and Classical Fields Vibration of Loaded String Vibrating Strings and the Wave Equation Continuous Systems and Classical Fields Scalar and Vector of Fields Appendix 1: Vector Analysis and Ordinary Differential Equations Appendix 2: D'Alembert's Principle and Lagrange's Equations Appendix 3: Derivation of Hamilton's Principle from D'Alembert's Principle Appendix 4: Noether's Theorem Appendix 5: Conic Sections, Ellipse, Parabola, and Hyperbola Index