View source for Principal normal

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A [[Normal|normal]] to a curve  $  L $
passing through a point  $  M _ {0} $
of  $  L $
and lying in the [[Osculating plane|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====
<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>