##### 2015-03-25

In this post, we build off the theory developed in Part 1 and actually implement a double-pendulum simulator in a few different programming languages. We'll start by writing our own Runge-Kutta solvers which will give us the position, velocity, and acceleration data that is needed to completely describe the trajectory of a double pendulum system given an arbitrary set of initial conditions. Once we have this data, we can move onto plotting it using a few different plotting libraries. The languages I'll be going over are Matlab, C++, and Python. I chose these languages because they are all quite popular and any given programmer is likely to understand at least one of them.

### Getting the Code

All of the code is hosted here on Github, and more details can be found at the Double-Pendulum-Simulation project page on my website. The entire project is available for download via either of these two links : .Tar , .Zip. You can also clone it straight from the command line :

git clone https://github.com/jhallard/Double-Pendulum-Simulation.git
cd Double-Pendulum-Simulation

### Quick Review

Below is a quick summary of the last post, for more information, read Part 1.

##### 2015-03-04

I've always thought that the double-pendulum makes an interesting system to simulate because the problem of doing so sits at the intersection of physics, mathematics, and computer science. The double-pendulum is also an approachable example of a chaotic system, which means it exhibits very complex and interesting behavior. Since I find it so interesting, I'll spend the next few posts writing about the topic. I'll start in this post with a derivation of the equations of motion and a look at the methods used to solve these equations. In the next post we'll actually solve these equations and implement the simulation in a few different programming languages, drawing performance and other comparisons along the way. Post 3 will wrap up this series with a deeper look into the complexities of the system, including an examination of its chaotic properties

The Double Pendulum - A snapshot at 5 seconds into my double-pendulum simulation in matlab