Clik here to view.
Dynamics of the 3-Body Problem
Recap In the last post we introduced the 3-body problem along with some constraints that turned it into the circular restricted 3-Body Problem (CR3BP). In the beginning of that post, I had a GIF that...
View ArticleClik here to view.
Chaos and the Double Pendulum
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...
View ArticleClik here to view.
Jacobi and his Constant – The 3-Body Problem
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...
View ArticleClik here to view.
An Introduction to Lagrange Points – The 3-Body Problem
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...
View ArticleClik here to view.
Forbidden Regions and where to Find Them – The 3-Body Problem
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...
View ArticleClik here to view.
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...
View ArticleClik here to view.
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...
View ArticleClik here to view.
Why Tracking Space Debris is so Hard
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...
View ArticleClik here to view.
Optimal Control of a Lunar Lander
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...
View ArticleClik here to view.
Periodic Orbits around Lagrange Points
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...
View Article