# Principal normal

From Encyclopedia of Mathematics

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:

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

#### Comments

#### 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 |

**How to Cite This Entry:**

Principal normal.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Principal_normal&oldid=48291

This article was adapted from an original article by E.V. Shikin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article