ANALYTICAL MECHANICS

3) Suppose we have the following form of the functional X2 J[y, z) = fly', z) dx, dy with the boundary conditions y(x) = Y, y(x)) = y2 . Here, y' = dx dz z' = Show that the extremum of this functional is given by the straight lines dx in three dimensions if Syyfez - (fyz) * # 0. Here partial derivatives are denoted byfy f for simplicity. " 3) Suppose we have the following form of the functional X2 J[y, z) = fly', z) dx, dy with the boundary conditions y(x) = Y, y(x)) = y2 . Here, y' = dx dz z' = Show that the extremum of this functional is given by the straight lines dx in three dimensions if Syyfez - (fyz) * # 0. Here partial derivatives are denoted byfy f for simplicity