here is the question, thank you.

Let A := {u = (u1, u2) : [0, 1] -> R2 | u E Cl} and consider the "holonomic constraints" problem: minimize Flu(.)] := Vuj (t) 2 + u') (t) 2 dt subject to: u E A, G(ul(t), u2(t)) := ul(t) + u2(t)2 - 1 = 0. (a) Thinking of this problem as a holonomic problem, find the Euler-Lagrange equations (you do not need to solve them). (b) Formulate the above problem as a problem without constraints and solve it. Hint: note that the holonomic constraint is just saying that ul (t) = 1 - u2(t)2. (c) Show that parts (a) and (b) give the same answer. Hint: what is A(t)