Hanging Chain
A project concerning variational ODE

Objective: Build a hanging chain apparatus. Measure physical shape and compare to ODE models.

Many variations possible: uniform or variable density, bending energies...

Aspects that could constitute significant (sub)projects:
(a) Mechanical (i.e., building the apparatus; designing chords of variable and measurable density).
(b) Numerical (i.e., producing a plot of numerically computed solutions which can be directly compared to the apparatus; this involves determining several parameters from the Euler-Lagrange equation).

Progress:

Fall 2001 (Deloughery, Leigh, Leonberg, Rogers) Analyzed hanging chain and hanging beam. Were unable to complete variational analysis for beam. Did, however, produce accurate plots for both (using force-balance equations in the case of the beam). Purchased beam at ACE Hardware and contacted manufacturer to get exact physical characteristics. Produced lifesize catenary for comparison to physical chain. Projected computed beam shape from transparency for comparison with 4 foot aluminum beam.

Fall 2002 (Paul Pearlman, Patryk Prus) Obtained energy for hangin slinky. Also, analyzed hanging chains.