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This paper deals with the concept of curvature of framed space curves, theirhigher-order derivatives, variations, and co-rotational derivatives. We realizethat parametrizing rotation tensor using the Gibbs vector is effective inderiving a closed form formula to obtain any order derivative of the curvaturetensor as the summation of functions of the parametrizing quantity and itsderivatives. We use these results for formulating a linearized updatingalgorithm for curvature and its derivatives when the configuration of the curveacquires a small increment. Finally, the MATLAB code to obtain updatedcurvature (spatial and material) and its derivatives is presented.

On the derivatives of curvature of framed space curve and their time-updating scheme: Extended version with MATLAB code