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  • Writer's pictureMayank Chadha, Ph.D.

On the derivatives of curvature of framed space curve and their time-updating scheme

Updated: Mar 15, 2023

Keyword: Lie Group, Material Frame, Curvature, Curvature Derivatives, Curvature Updating Algorithm

This article considers the curvature of framed space curves, their higher-order derivatives, variations, and co-rotational derivatives. We realize that parametrizing rotation tensor using the Gibbs vector is effective in deriving a closed-form formula that gives the general n-th order derivative of the curvature tensor as the summation of functions of the parametrizing quantity and its own derivatives. We use these results for formulating a linearized updating algorithm for curvature and its derivatives when the configuration of the curve acquires a small increment.

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