Bullet Nose

$\begin{figure}\begin{center}\BoxedEPSF{bullet_nose.epsf scaled 600}\end{center}\end{figure}$

A plane curve with implicit equation

$\begin{displaymath} {a^2\over x^2}-{b^2\over y^2}=1. \end{displaymath}$

(1)

In parametric form,

$\displaystyle x$	$\textstyle =$	$\displaystyle a\cos t$	(2)
$\displaystyle y$	$\textstyle =$	$\displaystyle b\cot t.$	(3)

The Curvature is

$\begin{displaymath} \kappa={3ab\cot t\csc t\over (b^2\csc^4 t+a^2\sin^2 t)^{3/2}} \end{displaymath}$

(4)

$\begin{displaymath} \phi=\tan^{-1}\left({b\csc^3 t\over a}\right). \end{displaymath}$

(5)

References

Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 127-129, 1972.