Welcome back to the Demonstration Highlight of the Week! This week, we’re taking a look at demonstration G1-60: Chaos with Two Bifilar Pendula. You can see the demonstration in action in this video featuring doctoral student Subhayan Sahu.

We have two essentially identical sets of physical pendulums suspended from a single rod. The physical laws governing their behaviour are quite simple, merely the conservation of linear and angular momentum and the force of gravity. The two pendulums are started into apparently identical oscillations, but starting the pendula with identical initial conditions is nearly impossible. So no matter what, their motion soon diverges. No matter how closely the motions of the two pendulums are started, they eventually must undergo virtually total divergence. This extreme sensitivity to initial conditions is a form of chaos, the mathematical study of irregularity in dynamical systems.

 Wikipedia has a surprisingly good article on the mathematics of the double pendulum. (https://en.wikipedia.org/wiki/Double_pendulum) Also, Eric Neumann has created an online simulation that can be used to model one of the legs of the pendulum. Try experimenting with the simulation as well, and see how sensitive it can be to its initial conditions. (https://www.myphysicslab.com/pendulum/double-pendulum-en.html)

There's a lot happening overhead this week!

The Perseid Meteor Shower is at its peak this week. Meteor showers are a stunning sight in the night sky, and the Perseids are one of the brightest of the year. The sparks of light you see in the sky are the burning debris from past passages of Comet Swift-Tuttle, which passes through the solar system every 133 years... but we pass through its path in August every year! Read more about the Perseids at NASA's Solar System Exploration pages.

Ordinarily, this would not have been the best of years to see the Perseids anyway, since the moon is full, and its bright light would make them hard to see. But it has turned out to be a moot point in our region, as our skies are darkened by a phenomenon much closer to home: Tropical Storm Isaias. This storm has been making its way up the coast and is now dumping quite a lot of rain on us, so everyone please be cautious! These storms can be dramatic to watch, but also potentially dangerous.

Hurricanes and tropical storms are driven by converging winds and moist air over warm water. Climate change in recent years has warmed the waters of the ocean - by only a small amount, but in a large and complex system, a small change in initial conditions can have a dramatic effect on the outcome! You can see this modeled in the classroom with demonstrations like our chaotic pendulum, G1-60; be sure to check out the simulation linked there that lets you experiment with tiny changes in the initial conditions. 

 Keep your eyes on the sky - but be careful out there!

Read more:

National Hurricane Center

NOAA video: Fuel for the Storm

NASA: In Depth on the Perseid Meteor Shower

EarthSky.org: Perseid Meteors 2020

Double Pendulum Simulator by Erik Neumann