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The Frenet–Serret formula is a formula describing the kinematic properties of a particle moving along a parametric curve. The formulas represent the derivatives of the function in terms of the basis formed by the tangent, normal, and binormal unit vectors. In matrix form, it is written as


\begin{bmatrix}
\tfrac{d\mathbf{\hat{T}}}{ds} \\

\tfrac{d\mathbf{\hat{N}}}{ds} \\

\tfrac{d\mathbf{\hat{B}}}{ds} \\
\end{bmatrix}

= 


\begin{bmatrix}
0 & \kappa & 0 \\

-\kappa & 0 & \tau \\

0 & -\tau & 0 \\

\end{bmatrix}

\begin{bmatrix}
\mathbf{\hat{T}} \\

\mathbf{\hat{N}} \\

\mathbf{\hat{B}} \\
\end{bmatrix}

with κ and τ representing the curvature and torsion, respectively.

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