For something more rigorous, I would like to take this opportunity to share rebound[1], something we use for n-body simulations in our field (planet formation). Perhaps few people here are already familiar with it. It has a Python interface but the C interface is very easy to use as well and has plethora of pre-set examples which can be visualized using GLFW. It's very very cool!

[1]https://github.com/hannorein/rebound