An optimal control formulation of the Blaschke-Lebesgue theorem
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Author
Contributions
- Naval Postgraduate School (U.S.). Dept. of Mathematics - Contributor
Publication
1988 - Naval Postgraduate School, Monterey, Calif, California
Language
English
Word Count
5,000 words, Guess
Page Count
20 pages
Identifiers
- Internet Archiveoptimalcontrolfo00ghan
- Open LibraryOL25481289M
Alternate Titles
- NPS-53-88-008.
Description
The Blaschke-Lebesgue theorem states that of all plane sets of given constant width the Reuleaux triangle has least area. The area to be minimized is a functional involving the support function and the radius of curvature of the set. The support function satisfies a second order ordinary differential equation where the radius of curvature is the control parameter. The radius of curvature of a plane set of constant width is non-negative and bounded above. Thus we can formulate and analyze the Blaschke-Lebesgue theorem as an optimal control problem. Keywords: Calculus of variation and optimal control. (KR) Limitation Statement:
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