Contents

• 0. Preface
• 0.1. N-Body Simulations
• 0.2. Ruby
• 0.3. Speed
• 0.4. Programming Issues
• 0.5. Acknowledgments
• 1. Setting the Stage
• 1.1. Ruby
• 1.2. A Body Class
• 1.3. The irb Interpreter
• 2. Introducing the Players
• 2.1. Creating a Body
• 2.2. Initializing a Body
• 2.3. Assigning New Values
• 2.4. Syntactic Sugar
• 3. Pretty Printing
• 3.1. Tinkering with the Output
• 3.2. A Body-to-String Converter
• 3.3. Taming the Arrays
• 3.4. Executing Ruby Files
• 4. Input and Output
• 4.1. Double Precision Input/Output
• 4.2. A Simple Version
• 4.3. Trying It Out
• 4.4. A Surprise
• 5. The Two-Body Problem
• 5.1. Equations of Motion
• 5.2. Relative Motion
• 5.3. Modularity
• 5.4. The First Integrator
• 5.5. Writing Clean Code
• 5.6. Where the Work is Done
• 6. Orbit Integration
• 6.1. Two Dimensions
• 6.2. Forward
• 6.3. Error Scaling
• 6.4. A Full Orbit
• 6.5. Taking Time
• 6.6. Convergence
• 7. Debugging
• 7.1. A Vector Class
• 7.2. Debugging
• 7.3. An Extra Safety Check
• 7.4. And Yet It Is
• 7.5. Using a Microscope
• 7.6. Following the Trail
• 7.7. Extreme Programming
• 8. Formula Translating
• 8.1. A Body with Vectors
• 8.2. Shrinking Code
• 8.3. FORTRAN
• 8.4. An Old Friend
• 8.5. Magic
• 8.6. A Matter of Taste
• 8.7. Voila
• 9. Energy Conservation
• 9.1. Estimating Numerical Errors
• 9.2. A Driver
• 9.3. The Body Class
• 10. Diagnostics
• 10.1. Evolve
• 10.2. Brevity and Modularity
• 10.3. Keeping Time
• 10.4. More Brevity
• 10.5. Ruby Smiling
• 10.6. A Here Document
• 11. Testing Forward Euler
• 11.1. Starting Again
• 11.2. Linear Scaling
• 11.3. A Full Orbit
• 11.4. Zooming In
• 11.5. Pericenter Passage
• 11.6. Apocenter Passage
• 12. Analytical Checks
• 12.1. Celestial Mechanics
• 12.2. The Role of the Masses
• 12.3. Reduced Mass
• 12.4. Wrapping It Up
• 13. Literature References