Principal normal

A normal to a curve $L$ passing through a point $M _ {0}$ of $L$ and lying in the osculating plane to $L$ at $M _ {0}$. If $\mathbf r = \mathbf r ( t)$ is the parametric equation of the curve and the value $t _ {0}$ corresponds to $M _ {0}$, then the equation of the principal normal in vector form is:

$$\mathbf r = \mathbf r ( t _ {0} ) + \lambda \mathbf r ^ {\prime\prime} ( t _ {0} ).$$

References

[a1]	D.J. Struik, "Lectures in classical differential calculus" , Dover, reprint (1988) pp. 13
[a2]	R.S. Millman, G.D. Parker, "Elements of differential geometry" , Prentice-Hall (1977) pp. 26