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