The inverse problem of variational calculus in two-dimensional Finsler space (Q910728)

The author deals with the inverse problem of the variational calculus in a parametric form. The problem is considered as a problem on Finsler metrics having the geodesics in a given form. Next the author finds the projectively flat Finsler metrics in \(R^ 2\) in the form \(L(x,y,\dot x,\dot y)=\dot x\int^{z}_{0}(z-t)H(t,y-tx)dt+\dot xE_ x+\dot yE_ Y\) where \(z=\dot x/\dot y\) and H, E are arbitrary functions.