9.12. Calculus of Variations with functionals involving two independent functions

So far, the functionals considered have contained only a single function and its first derivative. In this section, we will see how to approach a problem where the functional involves two independent functions.
In general, if we had n independent functions we would express our functional with matrix notations as follows:
J = ∫ t 0 T ( F ( t , y ( t ) , y ′ ( t ) ) d t
image (9.12-1)
s . t . y ( t 0 ) = y 0 and y ( T ) = y T
where:
y ( t ) ≜ [ y 1 ( t ) · · · y n

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