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I want to substitute ds by dt in the Frenet-Serret Formulas where κ is the curvature and is the torsion:

Tangential:[tex]\frac{d\vec{T}}{ds} = κ*\vec{N}[/tex]

Normal:[tex]\frac{d\vec{N}}{ds} = -κ*\vec{T}+τ*\vec{B}[/tex]

Binormal:[tex]\frac{d\vec{B}}{ds} =- τ*\vec{N}[/tex]

I want to substitute [tex]\frac{d\vec{T}}{ds} → \frac{d}{dt} T(t)[/tex] N(t), B(t) and solve for κ and τ.

Tangential:[tex]\frac{d\vec{T}}{ds} = κ*\vec{N}[/tex]

Normal:[tex]\frac{d\vec{N}}{ds} = -κ*\vec{T}+τ*\vec{B}[/tex]

Binormal:[tex]\frac{d\vec{B}}{ds} =- τ*\vec{N}[/tex]

I want to substitute [tex]\frac{d\vec{T}}{ds} → \frac{d}{dt} T(t)[/tex] N(t), B(t) and solve for κ and τ.

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