Rouben Rostamian | Miscellanea

Miscellanea

This page contains miscellaneous items and links which may or may not be of much significance or general interest. Browse to see if there is something useful here for you.

Stabilizing an inverted double-pendulum

Did you know that you can keep a double-pendulum pointing upward, that is, prevent it from falling, if you oscillate its pivot just right? The animation on the right demonstrates that.

The pivot, shown as a black diamond, oscillates vertically as y = Acos ωt. With a proper choice of amplitude A and angular frequency ω, the double-pendulum will remain upright while jittering chaotically. The system is quite stable—it won't fall if you gently push it.

The stabilizing effect of the pivot's oscillations in the case of a simple (that is, a single-link) pendulum was analyzed by the Russian physicist and Nobel laureate Pyotr Kapitsa in 1951; see the Wikipedia article about it. (No, he did not win the prize for solving this problem.) The general case of a compound pendulum of n links (n > 1) was analyzed by David Acheson in 1993.

On the Web you will find quite a few videos of actual physical experiments demonstrating this phenomenon. Search for “stabilizing an inverted pendulum”. Here is demo on YouTube. And here is another one.

UMBCposter

UMBCposter is a LaTeX documentclass for making research posters—the kind that one prints on large, A0-size paper and displays at meetings, conferences, and such.

I have made UMBCposter mostly for the use of our graduate students. But it's a free/open software, so you are welcome to try it. I make no guarantees that it will do anything useful for you. Don't blame me.

Beamer or Prosper?

Beamer and Prosper are utilities for creating presentation slides using LaTeX. Both are good packages so a choice between them is a personal decision. I started out using Prosper but now I use Beamer. Go to one of my tutorials on Beamer: A Quickstart or Prosper: a tutorial to learn more about them.

C Coding Style

The Linux kernel coding style was written by Linus Torvalds as a style-guide for his collaborators on developing and maintaining the Linux kernel. The advice in chapters 1–8 is generic and applies to any C programming project. I do follow that style myself, and recommend that you do it too.

Partial Fractions Done Right

If you have to do partial fractions by hand, you might as well do them the right way. Read Partial Fractions Done Right to find out how.

Dynagraph

Dynagraph is a graphics utility for plotting beautiful curves and surfaces. It is written entirely in C. The graphics are done in OpenGL and the user interface is done in xforms. It runs in the X Window System under Unix.

I wrote Dynagraph many years ago and I haven't done much to keep it up to date, or add features, or fix its (many) bugs. My plan is to rewrite it from scratch in Scheme and GTK+, when I find some free time. (When? It's been almost 20 years now…)

In the mean time, you may visit Dynagraph's Gallery and it if you find what you see there useful, then download the source and compile to run it on your computer.

Geometry

My Geometry page contains a motley collection of problems and puzzles of elementary geometry.

Humor

Penguins

There is no reason for having these photos here other than they are cute.

If you have seen the movie La Marche de l'empereur / March of the Penguins, you may think that the photos below are somehow related to that movie. But they are not. These were taken from Guillaume Dargaud's website http://www.gdargaud.net/Antarctica/Penguins.html long before that movie was made.

Ah, and this one…. I don't remember where I got it from. I will be glad to add credit if you know who made it.

[LoLpenguin.gif]