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…

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…

An Introduction to Error

Good Enough Numerical methods are always concerned with the term “good enough”. Whether you are using a finite difference to approximate a derivative, or Newtons method to find the roots of a function, we rarely get an exact answer. Usually, our answer is different from the truth by some amount. We generally don’t know what our error…