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Navigation Problem

A problem in the Calculus of Variations. Let a vessel traveling at constant speed $c$ 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.


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

© 1996-9 Eric W. Weisstein