On the derivatives of curvature of framed space curve and their time-updating scheme: Extended version with MATLAB code
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This paper deals with the concept of 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 to obtain any order derivative of the curvature tensor as the summation of functions of the parametrizing quantity and its 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. Finally, the MATLAB code to obtain updated curvature and its derivatives is presented.
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