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Introduction
Newtonian Dynamics
Richard Fitzpatrick
Professor of Physics
The University of Texas at Austin
Introduction
Intended Audience
Scope of Book
Major Sources
Newton's Laws of Motion
Introduction
Newtonian Dynamics
Newton's Laws of Motion
Newton's First Law of Motion
Newton's Second Law of Motion
Newton's Third Law of Motion
Non-Isolated Systems
Exercises
One-Dimensional Motion
Introduction
Motion in a General One-Dimensional Potential
Velocity Dependent Forces
Simple Harmonic Motion
Damped Oscillatory Motion
Quality Factor
Resonance
Periodic Driving Forces
Transients
Simple Pendulum
Exercises
Multi-Dimensional Motion
Introduction
Motion in a Two-Dimensional Harmonic Potential
Projectile Motion with Air Resistance
Charged Particle Motion in Electric and Magnetic Fields
Exercises
Planetary Motion
Introduction
Kepler's Laws
Newtonian Gravity
Conservation Laws
Polar Coordinates
Conic Sections
Kepler's Second Law
Kepler's First Law
Kepler's Third Law
Orbital Energies
Kepler Problem
Motion in a General Central Force-Field
Motion in a Nearly Circular Orbit
Exercises
Two-Body Dynamics
Introduction
Reduced Mass
Binary Star Systems
Scattering in the Center of Mass Frame
Scattering in the Laboratory Frame
Exercises
Rotating Reference Frames
Introduction
Rotating Reference Frames
Centrifugal Acceleration
Coriolis Force
Foucault Pendulum
Exercises
Rigid Body Rotation
Introduction
Fundamental Equations
Moment of Inertia Tensor
Rotational Kinetic Energy
Matrix Eigenvalue Theory
Principal Axes of Rotation
Euler's Equations
Eulerian Angles
Gyroscopic Precession
Rotational Stability
Exercises
Lagrangian Dynamics
Introduction
Generalized Coordinates
Generalized Forces
Lagrange's Equation
Motion in a Central Potential
Atwood Machines
Sliding down a Sliding Plane
Generalized Momenta
Spherical Pendulum
Exercises
Hamiltonian Dynamics
Introduction
Calculus of Variations
Conditional Variation
Multi-Function Variation
Hamilton's Principle
Constrained Lagrangian Dynamics
Hamilton's Equations
Exercises
Coupled Oscillations
Introduction
Equilibrium State
Stability Equations
More Matrix Eigenvalue Theory
Normal Modes
Normal Coordinates
Spring-Coupled Masses
Triatomic Molecule
Exercises
Gravitational Potential Theory
Introduction
Gravitational Potential
Axially Symmetric Mass Distributions
Potential Due to a Uniform Sphere
Potential Outside a Uniform Spheroid
Rotational Flattening
McCullough's Formula
Tidal Elongation
Roche Radius
Precession and Forced Nutation of the Earth
Potential Due to a Uniform Ring
Perihelion Precession of the Planets
Perihelion Precession of Mercury
Exercises
The Three-Body Problem
Introduction
Circular Restricted Three-Body Problem
Jacobi Integral
Tisserand Criterion
Co-Rotating Frame
Lagrange Points
Zero-Velocity Surfaces
Stability of Lagrange Points
Lunar Motion
Historical Background
Preliminary Analysis
Lunar Equations of Motion
Unperturbed Lunar Motion
Perturbed Lunar Motion
Description of Lunar Motion
The Chaotic Pendulum
Introduction
Basic Problem
Analytic Solution
Numerical Solution
Poincaré Section
Spatial Symmetry Breaking
Basins of Attraction
Period-Doubling Bifurcations
Route to Chaos
Sensitivity to Initial Conditions
Definition of Chaos
Periodic Windows
Further Investigation
Vector Algebra and Vector Calculus
Introduction
Scalars and Vectors
Vector Algebra
Cartesian Components of a Vector
Coordinate Transformations
Scalar Product
Vector Product
Rotation
Scalar Triple Product
Vector Triple Product
Vector Calculus
Line Integrals
Vector Line Integrals
Volume Integrals
Gradient
Grad Operator
Curvilinear Coordinates
Exercises
About this document ...
Richard Fitzpatrick 2011-03-31
