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{{Project|ACS}}

This is a wiki import, and, eventually, update of Piet Hut's and Jun Makino's [http://www.artcompsci.org/kali/pub/msa/title.html Moving Stars Around].

If you add or edit any pages below, at the top please include a link back to this page using the text:

<pre>
[[Moving Stars Around|Table of Contents]]
</pre>

0. [[MSA-Preface|Preface]]

1. [[MSA-The Universe in a Computer|The Universe in a Computer]]
# Gravity
# Galactic Suburbia
# Globular Clusters
# Galactic Nuclei
# Star Forming Regions
# Open Clusters
# Writing your own star cluster simulator
2. [[MSA-The Gravitational N-Body Problem|The Gravitational N-Body Problem]]
# Background
# Our Setting
# Fun and Profit
# What is the Problem, and why N and Bodies?
3. [[MSA-The Gravitational 2-Body Problem|The Gravitational 2-Body Problem]]
# Absolute Coordinates
# Coordinate Systems
# A Fourth Point
# Center of Mass
# Relative Coordinates
4. [[MSA-A Gravitational 1-Body Problem|A Gravitational 1-Body Problem]]
# Coordinates
# Equivalent coordinates
# Closing the Circle
# Newton's Equations of Motion
# An Equivalent 1-Body Problem
# Wrapping Up
5. [[MSA-Writing the Code-Ruby|Writing the Code (Ruby)]]
# Choosing a Computer Language
# Choosing an Algorithm
# Specifying Initial Conditions
# Looping in Ruby
# Interactive Ruby: irb
# Compiled vs. Interpreted vs. Interactive
# One Step at a Time
# Printing the Result
6. [[MSA-Running the Code-Ruby|Running the Code (Ruby)]]
# A Surprise
# Too Much, Too Soon
# A Circular Orbit
# Radial Acceleration
# Virial Theorem
# Circular Motion
# One Step at a Time
7. [[MSA-Debugging the Code-Ruby|Debugging the Code (Ruby)]]
# One Integration Step: Verification
# A Different Surprise
# One Integration Step: Validation
# More Integration Steps
# Even More Integration Steps
# Printing Plots
8. [[MSA-Convergence for a Circular Orbit-Ruby|Convergence for a Circular Orbit (Ruby)]]
# Better Numbers
# Even Better Numbers
# An Even Better Orbit
# Reasons for Failure
# Signs of Hope
9. [[MSA-Convergence for an Elliptic Orbit-Ruby|Convergence for an Elliptic Orbit (Ruby)]]
# Adding a Counter
# Sparse Output
# Better and Better
# A Print Method
# From One Body to Two Bodies
10. [[MSA-The Modified Euler Algorithm-Ruby|The Modified Euler Algorithm (Ruby)]]
# A Wild Idea
# Backward and Forward
# On Shaky Ground
# Specifying the Steps
# Implementation
# Experimentation
# Simplification
# Second Order Scaling
11. [[MSA-Arrays-Ruby|Arrays (Ruby)]]
# The DRY Principle
# Vector Notation
# Arrays
# Declaration
# Classes
12. [[MSA-Array Methods-Ruby|Array Methods (Ruby)]]
# An Array Declaration
# Three Array Methods
# The Methods each and each_index
# The map Method
# Defining a Method
# The Array#inject Method
# Shorter and Shorter
# Enough
13. [[MSA-Overloading the + Operator-Ruby|Overloading the + Operator (Ruby)]]
# A DRY Version of Modified Euler
# Not quite DRY yet
# Array Addition
# Who is Adding What
# The plus Method
# The + Method
# A Small Matter: the Role of the Period
# Testing the + Method
# A Vector Class
14. [[MSA-A Vector Class with + and --Ruby|A Vector Class with + and - (Ruby)]]
# Vector Subtraction
# Unary +
# Unary -
# An Unexpected Result
# Converting
# Augmenting the Array Class
# Fixing the Bug
15. [[MSA-A Complete Vector Class-Ruby|A Complete Vector Class (Ruby)]]
# Vector Multiplication
# An Unnatural Asymmetry
# Vector Division
# The Score: Six to One
# A Solution
# Augmenting the Fixnum Class
# Augmenting the Float Class
# Vector Class Listing
# Forward Euler in Vector Form
16. [[MSA-A Matter of Speed-Ruby|A Matter of Speed (Ruby)]]
# Slowdown by a Factor Two
# A C Version of Forward Euler
# A Simple Ruby Version
# A Ruby Array Version
# A Ruby Vector Version
# More Timing Precision
# Conclusion
17. [[MSA-Modified Euler in Vector Form-Ruby|Modified Euler in Vector Form (Ruby)]]
# An Easy Translation
# Variable Names
# Consistency
# A Method Returning Multiple Values
# Simplification
18. [[MSA-Leapfrog-Ruby|Leapfrog (Ruby)]]
# Interleaving Positions and Velocities
# Time Symmetry
# A Vector Implementation
# Saving Some Work
# The DRY Principle Once Again
19. [[MSA-Time Reversibility-Ruby|Time Reversibility (Ruby)]]
# Long Time Behavior
# Discussing Time Symmetry
# Testing Time Symmetry
# Two Ways to Go Backward
# Testing a Lack of Time Symmetry
20. [[MSA-Energy Conservation-Ruby|Energy Conservation (Ruby)]]
# Kinetic and Potential Energy
# Relative Coordinates
# Specific Energies
# Diagnostics
# Checking Energy
# Error Growth
# Pericenter Troubles
21. [[MSA-Scaling of Energy Errors-Ruby|Scaling of Energy Errors (Ruby)]]
# A Matter of Time
# A New Control Structure
# Overshooting
# Knowing When To Stop
# Linear Scaling
# Picture Time
22. [[MSA-Error Scaling for 2nd-Order Schemes-Ruby|Error Scaling for 2nd-Order Schemes (Ruby)]]
# Modified Euler
# Energy Error Scaling
# Leapfrog
# Another Error Scaling Exercise
# Roundoff Kicks In
23. [[MSA-Error Behavior for 2nd-Order Schemes-Ruby|Error Behavior for 2nd-Order Schemes (Ruby)]]
# Modified Euler: Energy Error Peaks
# Almost Too Good
# Leapfrog: Peaks on Top of a Flat Valley
# Time Symmetry
# Surprisingly High Accuracy
# Squaring Off
24. [[MSA-Literature References|Literature References]]