Friday, March 26, 2010

Hanging Chain with Varying Weights

Here's another hanging chain scenario. The red links are a little longer and much heavier.

Thursday, March 25, 2010

The Hanging Chain Problem - or Catenary

Here's a video from some software I just wrote for the class I've been taking part time (you should never stop learning!)



Here's my description of the problem from my report:

Consider a chain hung from the ceiling. How can we predict its
shape as it hangs? Each link in the chain will naturally fall until it
is pulled back by neighboring links. As the links fall, the potential
energy of the chain decreases until the chain has reached it’s final
shape.
If we minimize the potential energy of the whole chain, while keep-
ing the links connected, we can find this final shape. The most obvious
method to solve this problem would be to slowly attempt to move the
links of the chain downward without unlinking them. Each link would
move a little bit at a time, eventually reaching its final position.
However, such a method could be very slow - especially for large
chains. First of all, the actual movement of each link is restricted
by the neighboring links, meaning that only infinitesimal movements
could be made at a time. In addition, moving any link will affect every
other link in the chain.


I'll add a few details of my solution once everyone else has turned their projects in.