Next:
Introduction
An Introduction to Celestial Mechanics
Richard Fitzpatrick
Professor of Physics
The University of Texas at Austin
Introduction
Newtonian Mechanics
Introduction
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
Motion in a One-Dimensional Potential
Simple Harmonic Motion
Two-Body Problem
Exercises
Newtonian Gravity
Introduction
Gravitational Potential
Gravitational Potential Energy
Axially Symmetric Mass Distributions
Potential Due to a Uniform Sphere
Potential Outside a Uniform Spheroid
Potential Due to a Uniform Ring
Exercises
Keplerian Orbits
Introduction
Kepler's Laws
Conservation Laws
Polar Coordinates
Kepler's Second Law
Kepler's First Law
Kepler's Third Law
Orbital Energies
Kepler Problem
Orbital Elements
Binary Star Systems
Exercises
Orbits in Central Force-Fields
Introduction
Motion in a General Central Force-Field
Motion in a Nearly Circular Orbit
Perihelion Precession of the Planets
Perihelion Precession of Mercury
Exercises
Rotating Reference Frames
Introduction
Rotating Reference Frames
Centrifugal Acceleration
Coriolis Force
Rotational Flattening of the Earth
Tidal Elongation of the Earth
Tidal Torques
Roche Radius
Exercises
Lagrangian Mechanics
Introduction
Generalized Coordinates
Generalized Forces
Lagrange's Equation
Generalized Momenta
Exercises
Rigid Body Rotation
Introduction
Fundamental Equations
Moment of Inertia Tensor
Rotational Kinetic Energy
Principal Axes of Rotation
Euler's Equations
Eulerian Angles
Free Precession of the Earth
McCullough's Formula
Forced Precession and Nutation of the Earth
Exercises
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
Orbital Perturbation Theory
Introduction
Disturbing Function
Osculating Orbital Elements
Lagrange Brackets
Transformation of Lagrange Brackets
Lagrange's Planetary Equations
Transformation of Lagrange's Equations
Expansion of Lagrange's Equations
Expansion of Disturbing Function
Secular Evolution of Planetary Orbits
Hirayama Families
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
Useful Mathematrics
Conic Sections
Matrix Eigenvalue Theory
About this document ...
Richard Fitzpatrick 2011-04-22
