Nerd Sniping Myself #1
In this case, I end up down the rabbit hole of dynamical systems, and stability, and end up discovering some nice algorithmic art.
An Introduction to Stability
Note: This post is adapted from a lecture I gave to my undergrads. It’s focused on presenting the basics of stability for dynamical systems. The big question this lecture is intended to answer is what will our system do if we perturb it a small amount? This is not a rigorous treatment and in some…
Obtaining Equations of Motion: Newton vs Lagrange vs Hamilton
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…
Bennu, Osirus Rex, and JPL’s Small Body Database
On September 4th, 2023, a sample return canister will hopefully plummet through the skies of Utah. This sample return canister, after being charred due to the heat of atmospheric re-entry, will be brought to Johnston space center where scientists will open it to reveal up to 2 kilograms of the asteroid Bennu. This will mark…
Lunar Lander Optimal Control Using Dash
Disclaimer: Plotly paid me to both make a dash app, as well as this post. Even before this I was a fan of Plotly’s products and used them in posts about missed thrust events and visualizing periodic orbits. In those projects, I used Plotly because they make some great visualization tools. You should check their…
Psyche and Perturbations
Psyche For an orbital mechanics HW I was looking at Psyche and the effects of different perturbations. Psyche, an M-type asteroid, is one of the largest objects in the asteroid belt and contains about 1% of the belt’s entire mass. As an M-Type asteroid, Psyche is expected to be a reddish world mostly made up…
Ceres, Dawn, and JPL’s Small Body Database
Ceres In 2006, the International Astronautical Federation formally defined both planets and dwarf planets. “A “dwarf planet” is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, (c) has not cleared the…
Attracted to Attractors
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…
Core Dump #3 – 2020.01.06
Gereshes is now 2(ish) years old, so I figured it’s time for a quick Core Dump! Numbers In 2019 there were 54000 visitors to Gereshes that viewed 83000 pages. Not bad for such a math-heavy site! Last year only had 35 posts, with an average of 700 words per post. This ends up being about…
Main Branches of Astrodynamics
Earlier last week I was talking to one of my undergrads about the different subspecialties in astrodynamics and I’ve decided to distill that conversation into the following blogpost. Trajectory Design The best-known sub-specialty of astrodynamics, and the one that I’m in, is trajectory design. We answer questions like how do we get from Earth to…