An easy solution to it is made possible by the Beltrami identity, which can be applied to the Euler-Lagrange equations. It is analogous to the problem of a ray of light(*) passing through a medium in 
An easy solution to it is made possible by the Beltrami identity, which can be applied to the Euler-Lagrange equations. It is analogous to the problem of a ray of light(*) passing through a medium in which the index of refraction varies continuously. A problem of the calculus of variations with a solution given by a cycloid, for ten points, identify this problem of finding the curve that minimizes an object's falling time.
An easy solution to it is made possible by the Beltrami identity, which can be applied to the Euler-Lagrange equations.
brachistochrone problem