Chaos I’ve recreated one of my favorite mathematical demonstrations below. Three double pendulums, all starting with near identical initial conditions, all rapidly diverging. I love this demonstration because it’s such a great example of chaotic dynamics. What is Chaos? Chaotic dynamics, in a nutshell, means that a system is extremely sensitive to initial conditions. That…
Recap In the last post we introduced the 3-body problem along with some constraints that turned it into the circular restricted 3-Body Problem (CR3BP). In the beginning of that post, I had a GIF that traced out a trajectory in the Earth-Moon system. In this post, we will derive the equations of motion for the Circular…
Making a Lab a Home Engineering labs, like most work spaces, begin life as utterly functional sterile rooms. Sometimes they have cubicles, other times offices, and in a few rare occasions an open office layout, but they all begin sterile. Over time, the people who work there begin to fix it up and imbue within…
What is Journal club As a new grad student, I need to read a lot of papers. A rule of thumb for new grad students is to read 5-7 papers every week. As I read through them, I highlight statements, leave comments in the margins, and write up a small note about what I thought…
A Whole New Ballgame In the past, this blog has covered the 2-Body problem which is solvable (Kinda) and the general n-body problem which isn’t. We have a lot of insight into how the 2-body dynamics work, but unfortunately, they break down as soon as we get away from any major body. If you want…
Good Enough Numerical Methods are all about getting an answer that is good enough. A whole class of numerical methods are iterative methods, which continue running until they are good enough. Newton’s method is the example of an iterative method. It keeps going, making the error smaller and smaller until it finds a zero. A good…
Good Enough Numerical methods are always concerned with the term “good enough”. Whether you are using a finite difference to approximate a derivative, or Newtons method to find the roots of a function, we rarely get an exact answer. Usually, our answer is different from the truth by some amount. We generally don’t know what our error…
Bumpy Terrain Imagine you are halfway up a mountain. Half an hour ago you decided to start bushwhacking and now you’re completely turned around and lost. What’s worse is that you’ve also lost your map and compass. It’s getting late and you need to get back to your home at the foot of the mountain.…
Why Memory Cards are Useful Whenever a friend gets a camera, they usually come and ask me “What accessory should I get that will make me a better photographer?”. I’ll answer with two things, spare memory cards , and spare batteries. You don’t get better through better gear, you get better though practice. Practice in…
It’s a Book About Code, no not that Kind of Code While this book is titled “The Code Book”, it is not about computer science. It’s about a different type of science; “the science of secrecy”. How to hide messages and meaning, It’s about cryptography. The Code Book by Simon Singh is a 400-page book…
