Open AccessBicycle Routing for Maximum Suntan
Author(s) -
Geert Jan Olsder
Publication year - 2003
Publication title -
siam review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 4.683
H-Index - 120
eISSN - 1095-7200
pISSN - 0036-1445
DOI - 10.1137/s003614450139612
Subject(s) - maximum principle , euler's formula , path (computing) , simple (philosophy) , optimal control , mathematics , variable (mathematics) , constant (computer programming) , routing (electronic design automation) , calculus (dental) , mathematical optimization , computer science , mathematical analysis , medicine , philosophy , computer network , dentistry , epistemology , programming language
A simple optimal control problem is formulated in which one must find the optimal path along which to bike in order to get maximum suntan. Both the maximum principle and the Euler equation of the classical calculus of variations are used to calculate this optimal path. The interrelationship of the two approaches is elucidated; the adjoint variables in the maximum principle approach (which happen to be constants) are integration constants when solving via the Euler equation. Several slightly different versions of this problem are treated, with some surprising phenomena in the solution.
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