- #1

dIndy

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\int_0^{t_e}f(t)^2dt\int_0^{t_e}g(t)^2dt - (\int_0^{t_e}f(t)g(t)dt)^2

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With ## -1 \leq f(t)\leq1## and ## -1 \leq g(t)\leq 1## for all t

For this problem I can still intuitively guess a solution, such as: ## f(t)=1## for all t and ## g(t)=1## until ##0.5t_e##, afterwards ## g(t)=-1##.

But for more complicated problems I'll no longer be able to guess the solution and will need a proper way to find a solution. Most calculus of variations textbooks I've consulted (such as Gelfand) focus on problems that can be solved with the Euler-Lagrange equation, which I do not think can be applied here?

Does anybody know a textbook that covers these type of problems, or even a keyword that describes these kind of problems? Searching for calculus of variations did not get me far. I come from a life sciences background, so sadly my ability to read something much more complicated than the textbook by Gelfand is limited, but any recommendation is appreciated, thanks!