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.