Arising from the calculus of variations, the long way to solve it is to use the Euler-Lagrange differential equation, but one can use the Beltrami identity for a shortcut.  
Arising from the calculus of variations, the long way to solve it is to use the Euler-Lagrange differential equation, but one can use the Beltrami identity for a shortcut.  The parametric equations are identical to its solution and Newton's Second Law comes into play if one considers the effect of kinetic friction.  Greek for "shortest time," this famous problem was posed in the publication Acta Eruditorum by Johann Bernoulli and has a cycloid as its solution.  FTP, name this classic problem that seeks to find the minimal time it takes for a body under the force of gravity to get from one point to another.
Arising from the calculus of variations, the long way to solve it is to use the Euler-Lagrange differential equation, but one can use the Beltrami identity for a shortcut.  
brachistochrone problem