Luke Concini

The double pendulum is a chaotic system, meaning a unique lifetime is produced by slight alterations in initial conditions. For small-angle oscillations, a careful observer should be able to pick out an (approximate) superposition of normal modes!

This is a live RK4 numerical integration of a Hamiltonian state vector, using the bob angles as generalized coordinates q, and associated generalized momenta p. I used a very similar engine to simulate relativistic electron trajectories for my keV Electron Diode Source research project. Check out the poster, project, and report!

The n-body problem is given by finding the trajectories of n masses interacting through gravity. There is no analytic solution beyond 2 bodies, so this simulation uses direct force summation. See projects for work using similar techniques.

This simulation is inspired by Liu Cixin's novel The Three-Body Problem, featuring the Trisolarian planet (in blue) and the three suns of Trisolaris. It's neat to imagine the so-called 'Stable Eras' and 'Chaotic Eras' as the system evolves. Perhaps the 30 million-strong human computer in the story used the same algorithm!

The simple pendulum under small-angle conditions is a canonical example of simple harmonic motion, a keystone concept in many physical models.

While an approximation, using such simplifying cases to linearize a system is helpful when dealing with complex behaviour. It's a strategy I used extensively in PHYS 244: Classical Mechanics I; it was one of my favourite courses, unfortunately taken before I began using LaTeX to write my notes.