What are Cubesats? To answer that, let’s first define a U. A U is 10x10x10 cm cube of space from which cubesats derive their name. Cubesats are made up of multiples of these U’s put together and can have 1.33Kg of weight for every U in their structure. Cubesats can range from a simple 1U…
One Pendulum Less We’ve looked at the chaotic dynamics of double pendulums, but let’s take a moment to step back at the double pendulum’s simpler sibling, the single pendulum. This is the first post in a 3-part series looking at balancing an inverted pendulum Balancing an inverted pendulum – Part 1 Balancing an inverted pendulum…
Intro/Motivation One of the most common tasks in dynamics and controls is how do we get an object from point A to point B. Sometimes, like in the brachistochrone problem, we get lucky and there is a nice analytical solution. Unfortunately, in most situations, there is no closed form answer, and we need to turn…
Lissajous curves From orbits around Lagrange Points, to double pendulums, we often run into a family of loopy, beautiful, curves. These are called Lissajous curves, and describe complex harmonic motion. In layman terms, Lissajous curves appear when an object’s motion’s have two independent frequencies. Today, we’ll explore another system that produces Lissajous curves, a double…
1 Year Exactly 51 weeks ago, the first real Gereshes post came out. As of posting, 57 people have viewed it. In comparison, the most popular post from this year was viewed over 9000 times. It’s been a long year and a lot’s changed between those two posts. I figured I’d take this time between Christmas…
New Year, New Science Next week, as we ring in the new year, a spacecraft called New Horizons will push the boundary of human knowledge by being the first spacecraft to preform a close flyby of a Kuiper belt object. This isn’t the first time the grand piano sized spacecraft has embiggen human knowledge. From…
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…
Recap In the last two posts on what is the 3-body problem and the dynamics of the three body problem I’ve shown you the following GIF with a spacecrafts trajectory in the earth moon system. The trajectory is bouncing around what I’ve labeled a ‘forbidden region’. In this post we’ll go over the number behind…
