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Bicycle routing for maximum suntan. (English) Zbl 1023.49031

Summary: 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.

MSC:

49N90 Applications of optimal control and differential games
49K15 Optimality conditions for problems involving ordinary differential equations
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