ABSTRACT
To reach the extremum, based on the fundamental lemma, we need the solution of a set of n Euler-Lagrange equations of the form
∂f
∂yi − d
dx
∂f
∂y′i = 0; i = 1, . . . , n.
Most of the discussion insofar was focused on functions in explicit form. The concepts also apply to problems posed in parametric form. The explicit form variational problem of
I(y) =
f(x, y, y′)dx
may be reformulated with the substitutions
x = u(t), y = v(t).
