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Contents
[1]Title pagepdftitle
Analytical Classical Dynamics
An intermediate level course
Richard Fitzpatrick
Professor of Physics
The University of Texas at Austin
Contents
Introduction
Intended Audience
Major sources
Scope of Course
Outline of Course
Vectors
Introduction
Vector Algebra
The Scalar Product
The Vector Product
Rotation
The Scalar Triple Product
The Vector Triple Product
Vector Calculus
Line Integrals
Vector Line Integrals
Gradient
Useful Vector Formulae
Exercises
Fundamentals
Introduction
Fundamental Assumptions
Newton's Laws of Motion
Newton's First Law of Motion
Newton's Second Law of Motion
Newton's Third Law of Motion
Exercises
One-Dimensional Motion
Introduction
Motion in a General One-Dimensional Potential
Velocity Dependent Forces
Simple Harmonic Motion
Damped Oscillatory Motion
Resonance
Periodic Driving Forces
Transients
The Simple Pendulum
Exercises
Multi-Dimensional Motion
Introduction
Motion in a Two-Dimensional Harmonic Potential
Projectile Motion with Air Resistance
Motion in Crossed 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
The 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
Non-Inertial Reference Frames
Introduction
Rotating Reference Frames
Centrifugal Acceleration
The Coriolis Force
The Foucault Pendulum
Exercises
Rigid Body Motion
Introduction
Fundamental Equations
The Moment of Inertia Tensor
Rotational Kinetic Energy
Matrix Theory
The 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
The Spherical Pendulum
Exercises
Hamiltonian Dynamics
Introduction
The 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
Mathematical Digression
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
Precession of the Equinoxes
Potential Due to a Uniform Ring
Perihelion Precession of the Planets
Perihelion Precession of Mercury
Exercises
The Three-Body Problem
Introduction
The Circular Restricted Three-Body Problem
The Jacobi Integral
The Tisserand Criterion
The Co-Rotating Frame
The Lagrange Points
Zero-Velocity Surfaces
Stability of Lagrange Points
The Chaotic Pendulum
Introduction
Analytic Solution
Numerical Solution
The Poincaré Section
Spatial Symmetry Breaking
Basins of Attraction
Period-Doubling Bifurcations
The Route to Chaos
Sensitivity to Initial Conditions
The Definition of Chaos
Periodic Windows
Further Investigation
About this document ...
Richard Fitzpatrick 2008-01-13
