Cycloalkanes Directory Reference

The cyclohexane, cycloheptane, and cyclooctane.

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Files
file	Cycloheptane.world [code]
	A cycloalkane with a 7 carbon loop.
file	Cyclohexane.world [code]
	A cycloalkane with a 6 carbon loop.
file	Cyclooctane.world [code]
	A cycloalkane with a 8 carbon loop.

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Detailed Description

The cycloalkanes are molecules that include a loop of carbon atoms. The presence of a loop constraint makes CuikSuite specially adequate tool to analyze their conformational space.

Note that the formulation we use here for the cycloalkanes is not based on distances (as we did in our JCC paper), but on vectors and rotation matrices, as in our more recent TRO paper.

Moreover, not that in the formulation of the cycloalkanes, we use a variant of the formulation described in our recent TRO paper. We do not use orthonormal reference frames for the links but we use the two vectors aligned with the rotation axis coincident in each carbon to defined a non-orthogonal reference frame. This produces equation sets that can be easily simplified avoiding numerical issues.
The generalization to use non-orthonormal reference frames whe it is advantageous is applied in general and not only in these examples, howerver the effect is specially relevant in the cycloalkanes.

References

• J. M. Porta, L. Ros, F. Thomas, F. Corcho, J. Cantó,J. Pérez, "Complete Maps of Molecular Loop Conformational Spaces", Journal of Computation Chemistry, Vol. 28, pp. 2170-2189, 2007.
• J. M. Porta, L. Ros, and F. Thomas, "A Linear Relaxation Technique for the Position Analysis of Multi-loop Linkages", IEEE Transactions on Robotics, accepted for publication, 2008.