MisterX
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We seek stationary solutions to
[itex]\int_{x_0}^{x_1} F(x, y, y')dx[/itex]
subject to the constraint
[itex]\int_{x_0}^{x_1} G(x, y, y')dx = c[/itex]
where [itex]c[/itex] is some constant.
I have read that this can be solved by applying the Euler Lagrange equations to
[itex]F(x, y, y') + \lambda G(x, y, y')[/itex]
and then finding the appropriate value of [itex]\lambda[/itex] when solving so that the constraint is satisfied.
Why does this work? I am not sure what reference to use.
Also, this may still work when the unconstrained integral has no stationary solutions, right?
[itex]\int_{x_0}^{x_1} F(x, y, y')dx[/itex]
subject to the constraint
[itex]\int_{x_0}^{x_1} G(x, y, y')dx = c[/itex]
where [itex]c[/itex] is some constant.
I have read that this can be solved by applying the Euler Lagrange equations to
[itex]F(x, y, y') + \lambda G(x, y, y')[/itex]
and then finding the appropriate value of [itex]\lambda[/itex] when solving so that the constraint is satisfied.
Why does this work? I am not sure what reference to use.
Also, this may still work when the unconstrained integral has no stationary solutions, right?