Undergrad Calculus of Variations Dependent variables and constraints

[shedrick94]

If we have a function:

\begin{equation} f(x,x',y,y',t) \end{equation} and we are trying to minimise this subject to a constraint of
\begin{equation} g(x,x',y,y',t) \end{equation}

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)??

 

[drvrm]

and we are trying to minimise this subject to a constraint of.

g(x,x′,y,y′,t)​

(2)(2)g(x,x′,y,y′,t)\begin{equation} g(x,x',y,y',t) \end{equation}

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

pl. give explicit eq of constraint -that will define the set of generalized coordinates.