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…
A Quick Estimate A few days ago I was invited to take part in a mock architecture study looking at Deep Space CubeSat missions. As a multi-body dynamics fanboy, my heart jumped at the possibility of using the interplanetary superhighway to preserve our meager delta-V budget. The downside of using the interplanetary superhighway is that…
Everything Orbits About Something In our solar system, Moons orbit around planets, which themselves orbit around the sun. Well, actual they orbit about the system barycenter, the combined center of mass between the two bodies. But can we get an object to orbit around a region without a barycenter? Yes! (Kinda) There are actually a…
Recap of Lagrange Points In the circular restricted three body problem, there are a set of 5 points that if we place our spacecraft there, it’ll never move relative to the two bodies. These are called the Lagrange points and are the only equilibrium points for the system. Whenever we find an equilibrium point in…
Jacobi and Lagrange So far we have explored the Jacobi Integral and the Lagrange points. Now, we are ready to combine the two into one of the most useful concepts in the Circular restricted 3-Body Problem (CR3BP), forbidden regions. You’ve seen them in my visualizations before, but now we’ll finally go over what they are.…
Balancing a Marble Imagine you had a marble and you wanted to put it at the point between the Earth and the Moon where the force of gravity was equal from both. The two forces would cancel out, and the marble would remain in that location forever. If the sun and the earth were not…
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…
