A couple of years ago, I had to make a catapult as part of an elective in high school. This project got me thinking about how someone might try to predict the performance of one of these contraptions before they committed to building it. I did some research and found out about dynamic systems and the Lagrange equations. Here, I derive these equations and relate them to the topic of functional derivatives and the action integral. I also show how they can be applied to a theoretical trebuchet using Matlab!
In doing a little research, I found a webpage by Donald Siano where he has written a more robust piece of software for making trebuchet calculations. He also has a paper in which he describes the algorithms he has used, which are based on the Lagrange equations. His paper details the algorithmic treatment of more complex trebuchets in much the same way I have treated a simple one. A link to his paper is:
Trebuchet Mechanics by Donald Siano
a free GUI-based program that performs these simulations can be found on his website:
The Algorithmic Beaty of the Trebuchet
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