Chernowitz, D (2014) Optimal Road Problem. Bachelor's Thesis, Mathematics.
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Abstract
We consider the problem of paving a path through a mountainous terrain. An optimal path is one that balances the requirement of a route to be both as short as possible and as flat as possible. A new form of Riemannian metric, $tilde{S}$, is proposed to weigh the length of a path, such as to penalize vertical transport more than horizontal, reflecting the cost and difficulty of traffic to change altitude. A geodesic $boldsymbol{gamma}$ of this metric is then a candidate for an optimal path. A number of numerical solution techniques to calculate geodesics are explored, most notably a functional iteration using Christoffel's symbols of the geodesic equation, and geodesic evolution to minimize geodesic curvature. Finally, statistical analyses are done on the resulting geodesics of this weighted metric through a simulated hilly landscape. The metric performs well in balancing horizontal versus vertical travel economically, however it does not prevent a high maximum steepness over the course of the path.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 15 Feb 2018 07:56 |
| Last Modified: | 15 Feb 2018 07:56 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/11595 |
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