Polar tangential angles and free elasticae

Tatsuya Miura; Tatsuya Miura

doi:10.3934/mine.2021034

Mathematics in Engineering

2021, Volume 3, Issue 4: 1-12. doi: 10.3934/mine.2021034

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Polar tangential angles and free elasticae

Tatsuya Miura ^,

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

Received: 13 April 2020 Accepted: 29 April 2020 Published: 21 August 2020

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.
- polar tangential angle,
- monotone curvature,
- free elastica,
- obstacle problem
Citation: Tatsuya Miura. Polar tangential angles and free elasticae[J]. Mathematics in Engineering, 2021, 3(4): 1-12. doi: 10.3934/mine.2021034

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Abstract

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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