# DAY 2

# Lecture Notes

#### Day 2 Intro Slides

Reminder of what we have done/some intro to what we are doing today.

#### Day 2 Intro Slides (Part 2)

A reminder of what we have discovered so far: the importance of the time step! Lets think about conserved quantities...

#### Day 2 Intro Slides (Part 3)

A reminder of what we have discovered so far: the importance of the time step! Testing the "goodness" of our numerical simulation! Can we do better...

# Code

#### Plot Analytical + Numerical 2-Body Problem + Indexing Hints

Some python code for plotting an elliptical solution for the 2-Body problem from Day 1. Some hints for setting up indexing for each planet.

#### Plot Analytical + Numerical 2-Body Problem (Mine)

Some python code for plotting an elliptical solution for the 2-Body problem from Day 1. This includes the analytical solution and code for how I set up numerical integration with a Euler's-type integration scheme. Your setup might be different and that is ok!

#### Plot Analytical + Numerical 2-Body Problem with Energy & Momentum

Some python code for plotting an elliptical solution for the 2-Body problem. This includes the analytical solution and some code for setting up numerical integration with a Euler's-type integration scheme. Code for including plots of energy and angular momentum are included as well.

#### Some code that compares Hermite and Euler Integration Schemes with Analytical

Python code comparing different methods of integration for the 2-Body problem.

# Resources

#### Some 2-Body Problem Notes

Some notes on the 2-Body problem from Massimo Ricotti's computational astrophysics class.

#### Notes on Integration in N-body

Some notes on general integration of N-Body problems from Massimo Ricotti's computational astrophysics class.

#### Integration of ODE's

Some notes on integration methods for ordinary differential equations from Massimo Ricotti's computational astrophysics class.

#### Indepth Discussion of Several Integrators

Goes over some pros/cons of different sorts of integrators. Hermite integrators are discussed in section 2.3.2.