Navigation Problem

A problem in the Calculus of Variations. Let a vessel traveling at constant speed navigate on a body of water having surface velocity

$\displaystyle u$	$\textstyle =$	$\displaystyle u(x,y)$
$\displaystyle v$	$\textstyle =$	$\displaystyle v(x,y).$

The navigation problem asks for the course which travels between two points in minimal time.

References

Sagan, H. Introduction to the Calculus of Variations. New York: Dover, pp. 226-228, 1992.