Calculating the Stationary Value of J Integral

In summary, the stationary value of J subject to the constraint of \phi is given by the free variation of I, which can be expressed as \delta I = \int_{a}^{b}dt~\left[\frac{\partial F}{\partial x} \delta x \frac{\partial F}{\partial \dot{x}} \delta{\dot{x}}\right]. This can be further explored using the concept of Lagrange multipliers.
  • #1
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Homework Statement

Show the stationary value of,



subject to the constraint,



is given by the free variation of,



The attempt at a solution

Not sure where to start here; or really what's wanted... Do I start with and and get to the variation of ?

Is the free variation of given by,

?
 
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  • #2
It's been a while since I did this, but you may want to take a look at "Lagrange multipliers", that might get you on track.
 
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