View source for Principal normal

A [[Normal|normal]] to a curve <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074750/p0747501.png" /> passing through a point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074750/p0747502.png" /> of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074750/p0747503.png" /> and lying in the [[Osculating plane|osculating plane]] to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074750/p0747504.png" /> at <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074750/p0747505.png" />. If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074750/p0747506.png" /> is the parametric equation of the curve and the value <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074750/p0747507.png" /> corresponds to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074750/p0747508.png" />, then the equation of the principal normal in vector form is:

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074750/p0747509.png" /></td> </tr></table>



====Comments====


====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  D.J. Struik,   "Lectures in classical differential calculus" , Dover, reprint  (1988)  pp. 13</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  R.S. Millman,   G.D. Parker,   "Elements of differential geometry" , Prentice-Hall  (1977)  pp. 26</TD></TR></table>