Connected springs can be described approximately with simultaneous linear equations. As long as the springs don't rotate much, the equations can be solved quickly. But because the ladder wants to curl, each solution to the equations causes a lot of springs to rotate, resulting in a new set of equations that needs to be solved, and so forth. This applet does manage to curl the ladder into a nice quiet hexagon in five or ten minutes. But I'm hoping for a still more powerful method.
Once again, you can start the applet over by scrolling to the top and hitting the browser's reload button.
The source for the first applet is FastMech.java; for the second applet, FastMech2.java.