Analytical Solution for the Generalized Fermat-Torricelli Problem

Abstract

We present explicit analytical solution for the problem of minimization of the function $F(x,y)={\sum }_{j=1}^3{m}_j\sqrt{(x-x_j{)}^2+(y-y_j{)}^2}$, i.e. we find the coordinates of stationary point and the corresponding critical value of $F(x,y)$ as functions of ${m_j,x_j,y_j}_{j=1}^3$. In addition, we also discuss inverse problem of finding such values of $m_1,m_2,m_3$ with the aim for the corresponding function $F$ to posses a prescribed position of stationary point.

arXiv comment15 pages, 3 figures