hlp from my diff. geo. book i dun get it:

Let κ(s) (>0) and τ(s) be continuous functions of a real variable s, defined in an interval I: 0≤s≤a. The formulae of Frenet

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are three systems of ordinary linear differential equaations of the unit vectors t, the unit tangent vector, p, the principle normal unit vector, and b, the binormal unit vector, of the moving trihedron,

(20.1) Log in to see images!

For the sake of simplicity, we set

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Therefore we have, written in vector form, differential equations of the type

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We write these equations again in scalar form, omitting the index i by which the different components of the vectors Log in to see images! are denoted, that is, we write (20.1) in the form

(20.1’ ) Log in to see images!

In (20.1’ ) the elements of the coefficient matrix

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are continuous functions in the closed interval I: 0≤s≤a and consequently bounded in I,

(20.2) Log in to see images!