Jump to content
Sign in to follow this  
  • entries
  • comments
  • views

Pendulums Are Weird

Sign in to follow this  


Pendulums seem fairly simple, right? You take some mass, you take some string, throw them in a gravitational field, and bam! It goes back an forth, back and forth, back and forth. Without any kinds of friction, this will continue forever!

But, what if you take a pendulum, and then stick a pendulum on the end of that pendulum? Well basically, things get incredibly more complicated. For a single pendulum, especially one that has a small angle of oscillation, you can predict exactly where it will be in its cycle virtually infinitely far into the future. However for even a double pendulum, this becomes impossible, without calculating every single intermediate state of the pendulum. And the motion of multi-pendulum systems is incredibly complicated in and of itself - for an n-pendulum system, one must solve an n-dimensional system of equations do calculate the motion of each pendulum, involving the momenta, kinetic energy, and potential energy of each of the individual components of the system. Basically, multi-pendulums are hard.


From https://en.wikipedia.org/wiki/Double_pendulum

Another property of these systems is that they are so-called "chaotic," meaning that a small change in the initial conditions can lead to large changes in the end result of the system, especially as time goes on. For instance, say you have two double pendulums set up. You start them both at just about the same place, but offset the second one by a single degree from the first one. Initially they may follow very similar paths, but as time goes on, it will seem as if they could have started from completely different initial conditions. Chaos appears all over nature and mathematics.

Sign in to follow this  

1 Comment

Recommended Comments

Add a comment...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Terms of Use

The pages of APlusPhysics.com, Physics in Action podcasts, and other online media at this site are made available as a service to physics students, instructors, and others. Their use is encouraged and is free of charge. Teachers who wish to use materials either in a classroom demonstration format or as part of an interactive activity/lesson are granted permission (and encouraged) to do so. Linking to information on this site is allowed and encouraged, but content from APlusPhysics may not be made available elsewhere on the Internet without the author's written permission.

Copyright Notice

APlusPhysics.com, Silly Beagle Productions and Physics In Action materials are copyright protected and the author restricts their use to online usage through a live internet connection. Any downloading of files to other storage devices (hard drives, web servers, school servers, CDs, etc.) with the exception of Physics In Action podcast episodes is prohibited. The use of images, text and animations in other projects (including non-profit endeavors) is also prohibited. Requests for permission to use such material on other projects may be submitted in writing to info@aplusphysics.com. Licensing of the content of APlusPhysics.com for other uses may be considered in the future.

  • Create New...