# Calculus of Variations Dependent variables and constraints

• I
If we have a function:

$$f(x,x',y,y',t)$$ and we are trying to minimise this subject to a constraint of
$$g(x,x',y,y',t)$$

Would we simply have a set of two euler lagrange equations for each dependent variable, here we have x and y.

Would we insert f(x,x',y,y',t)-Ag(x,x',y,y',t) into both equations, where A is a constant? Or would each equation require a different constant in front of the constraint term g(x,x',y,y',t)??

(2)(2)g(x,x′,y,y′,t)$$g(x,x',y,y',t)$$