The Algorithmic Beauty of the Trebuchet

# lagrangederivations.nb A Mathematica Notebook with the derivations for all of the equations required for input to the MacTreb* and WinTrebstar applications.

To use it copy the notebook to the clipboard, then open mathematica, then open a new notebook, and paste the clipboard in.

This is for the record and the posterity of mankind: the complete derivations for the second derivatives of the angles for use with a numerical differential equation solver. But don't bother with this unless you have Mathematica or MathReader. (63 k)



The Numerical Method

Here are the basic formulas I use to solve the differential equations:
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JavaScriptTreb

Eat your heart out wintreb!

A trebuchet calculatorbased on the mathematica expressions, translated into javascript for the unconstrained (no sliding) trebuchet that has a sling and a hinged counterweight. Similar in spirit to wintreb, but is platform independent (sorta) and all the assumptions and methods are available for study and improvement. Use this if you are interested in designing a treb of your own. Or in understanding one you've already built!

An animated treb. Hit the button.


Some other informative graphical representations of the movement of parts of the trebuchet.

Monte Carlo Fortran Listing

A Monte Carlo optimization program. Here is the Fortran program listing and output for the unconstrained treb with a sling and a hinged counterweight. Very fast. Allows the exploration of thousands of designs in a matter of minutes.



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