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3D Pebble Game with Central Forces and Angular Forces
Although the Laman condition remains unproven in three dimensions,
it has been shown that it can be generalized within bond bending
networks [1,2], via the Molecular Framework Conjecture. If A,B and
C are vertices, then such networks have an angular force
associated with the angle ABC (or equivalently a central force
AC), everywhere there are central forces connecting AB and BC. No
counter-examples have been found to this conjecture, and it is
strongly believed to be correct, but still awaits a formal
proof. The development of this routine was originally due to
D.J. Jacobs and M.F. Thorpe, with subsequent input from Mykyta
Chubynsky [3,4]. The 3D Pebble Game program can be
downloaded. Using three pebbles, the program finds the total
number of floppy modes; decomposes the network into rigid clusters
and identifies those parts of the rigid clusters that are
over-constrained (stressed). An illustrative example, comes in a
separate directory, where there is a description of how to build
the network, the input files and a description of the output
files.
Download the source code
pebble_3D_CF_and_AF.tar.gzThe following link contains examples of using the above source code. The files are tarred and gzipped. pebble_3D_CF_and_AF_examples.tar.gz Files available for download.
Download a brief description of the 3D pebble game algorithm for bar-joint networks.3D_CF_and_AF_description.pdf References
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