Note: This post is adapted from a lecture I gave to my undergrads. It’s focused on conveying the method and main idea behind the different formulations. This is not a rigorous treatment and in some locations, I have traded being technically correct for being clear. If you want a riggorous treatment of the material I…
What are Attractors Attractors, in dynamical systems are structures that a lot of initial conditions evolve to over time. When the dynamics are chaotic, if an attractor exists, they often have a fractal structure which makes them gorgeous to visualize and are called strange attractors. Below are three, 3-dimensional strange attractors as well as the…
A while ago I set up SpaceBot, a twitter bot designed to post about space. In the meantime, I’ve rolled out some upgrades to it. Here they are, What Happened in Deep Space Today By looking at Jonathan McDowell’s deep space catalog, SpaceBot now posts a random event that happened that day in deep space…
Introduction NOTE: This is a very graphics-heavy post and may take some time to load. Lagrange points are those points in the three-body system where the tug of gravity from the two primary bodies cancel out and any spacecraft stays in the same relative position with the two primary bodies. If you are in the rotating…
Intro Last year we had a 2 part series on how to land on the moon using a suicide burn. There, the condition was that we could only turn on the engine once, and it had to be fully throttled. But most landers can control their thrust, so in this post we’re going to go…
Once you derive the equations of motion for a system, the next step in simulating it numerically is to compute the state-space representation, the backbone of modern contorl theroy. This is useful because by placing the equations of motion in a common format we can apply a whole host of techniques to study the system.…
A few weeks ago I attended the 2019 AAS/AIAA Astrodynamics Specialists Conference (ASC). This was my first major academic conference in grad school and I was there presenting on my research on using neural networks for optimal control with a special focus on their resilience to missed thrust events. Where Was I? The Astrodynamics Specialist…
Inverted Pendulum Recap In this post, we’re going to talk a little about how to balance an inverted pendulum on a cart. This is the second post in a 3 part series about balancing an inverted pendulum Part 1 – Balancing an inverted pendulum Part 2 – Swing-Up of an Inverted Pendulum on a Cart…
Space Debris From dead satellites to flecks of paint, there are over 500,000 pieces of space debris currently being tracked. Space debris, and the problems they can cause is a hot topic with everything from a major Hollywood movie to TED talks being given about them. In this post I’m going to go over a less…
Picture This Humans are a visual species, we look for patterns in life and we are great at finding them when they are visual. We can tell two people apart just by looking at their faces. Sometime’s we’re too good at seeing patterns and we see faces in a piece of burnt toast. If we’re…
