Definition:Extremal Embedding in Field of Functional
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Definition
Let $J$ be a functional such that:
- $\ds J \sqbrk {\mathbf y} = \int_a^b \map F {x, \mathbf y, \mathbf y'} \rd x$
Let $\gamma$ be an extremal of $J$.
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Let $R$ be a simply connected open region which contains $\gamma$ as a subset.
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Let a field of functional $J$ be defined at every point of $R$.
Let one of the trajectories of the field be $\gamma$.
Then $\gamma$ can be embedded in a field of functional $J$.
This article, or a section of it, needs explaining. In particular: If $\gamma$ "can be" embedded, is it correct to say that $\gamma$ "is" embedded? If not, then is it more grammatically accurate to define $\gamma$ as being "embeddable"? Otherwise it looks as though "can be" introduces a statement that needs to be proven. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code. |
Sources
- 1963: I.M. Gelfand and S.V. Fomin: Calculus of Variations ... (previous) ... (next): $\S 6.32$: The Field of a Functional