# Tagged Questions

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### fundamental optimal-trajectory result known?

It's well-known and obvious that if you have a spaceship and your sole constraint is an upper bound on magnitude of acceleration/deceleration, the fastest way to get to a distant star (a fixed ...
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### Approximating solutions to minima of the discrete Lagrangian

I have been stuck on this problem for a week and I'm not sure whether or not it is hard or I'm just missing something obvious. General gist of the problem I have a variational problem on a ...
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### Minimizing action squared versus action

I have a very basic question in the calculus of variations: Suppose I want to minimize the functional $$A[r, r'] = \int_\Omega L(r, r') dx$$ When is it possible to say that extremals of $A$ agree ...
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### A Lagrangian problem with a countable family of local extrema ?

Dear MO contributors, let $r > 0, L > 0$. I am interested in maximizing the integral: $$\int_0^{2\pi} \frac{f(\alpha)^2 f'(\alpha)^2}{\sqrt{f(\alpha)^2 + f'(\alpha)^2}} \ \mathrm{d} \alpha$$ ...
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### Equitable division of a contiguous resource

I have come across the following result regarding equitable division of a resource, which is a simple and immediate consequence of linear programming complementarity (in the infinite-dimensional ...