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Polar tangential angles and free elasticae

Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan

This contribution is part of the Special Issue: Geometric Partial Differential Equations in Engineering
Guest Editor: James McCoy
Link: www.aimspress.com/mine/article/5820/special-articles

Special Issues: Geometric Partial Differential Equations in Engineering

In this note we investigate the behavior of the polar tangential angle of a general plane curve, and in particular prove its monotonicity for certain curves of monotone curvature. As an application we give (non)existence results for an obstacle problem involving free elasticae.
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Keywords polar tangential angle; monotone curvature; free elastica; obstacle problem

Citation: Tatsuya Miura. Polar tangential angles and free elasticae. Mathematics in Engineering, 2021, 3(4): 1-12. doi: 10.3934/mine.2021034

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