Chaotic Swirls and the Duffing Equation
Springs, Except More Fun In any introductory physics or differential equation’s class we are introduced to the simple spring mass system. Because of Hooks law it’s nice, linear, and easy to analyze. But not all springs follow Hooks Law. Some, like the duffing spring we’ll analyze in this post, are nonlinear and chaotic. What’s a…
Lyapunov Orbits
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…
An Introduction to CubeSats
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…
Balancing an Inverted Pendulum
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…
An Introduction to Shooting Methods
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…
Double Spring Mass Systems & Matlab’s ODE 45
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…
Core Dump #2 – 2018.12.31
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…
A Re-Introduction to New Horizons
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…
Stability of the Lagrange Points – Three Body Problem
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…