this is an euler lagrange equation problem from the book- "classical mechanics-John R. Taylor", problem-6.11
find the path function for which ∫ √x*√(1+y'^2) dx is stationary.
the answer is- x= C+(y-D)^2/4C, the equation of a parabola.
here the euler lagrange equation will work on f=√x*√(1+y'^2).
since ∂f/∂y= 0, so ∂f/∂y'= const
→ √x*y'/ √(1+y'^2)= constant.
then i dont get how i get from here to the equation of the parabola.
any help?
find the path function for which ∫ √x*√(1+y'^2) dx is stationary.
the answer is- x= C+(y-D)^2/4C, the equation of a parabola.
here the euler lagrange equation will work on f=√x*√(1+y'^2).
since ∂f/∂y= 0, so ∂f/∂y'= const
→ √x*y'/ √(1+y'^2)= constant.
then i dont get how i get from here to the equation of the parabola.
any help?