# American Institute of Mathematical Sciences

October  2015, 8(5): 1009-1022. doi: 10.3934/dcdss.2015.8.1009

## Towards modelling spiral motion of open plane curves

 1 Department of Mathematical Sciences, School of Science and Technology, Kwansei Gakuin University, 2-1 Gakuen, Sanda 669-1337, Japan 2 Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashi-Mita, Tama-ku, Kanagawa 214-8571

Received  January 2014 Revised  June 2014 Published  July 2015

We propose a simple evolution law for the motion of open curves with the boundary conditions towards realizing spiral growth, and derive the so-called kinematic equation. The role of the tangential velocities is studied and proved that they can be chosen arbitrarily for given boundary values. From this fact, a curvature adjusted tangential velocity for open curves is introduced. We present a numerical example which provides spiral motion starting from a line segment. This is a contrast to the case where an expanding line segment is the exact solution without the boundary conditions.
Citation: Koichi Osaki, Hirotoshi Satoh, Shigetoshi Yazaki. Towards modelling spiral motion of open plane curves. Discrete & Continuous Dynamical Systems - S, 2015, 8 (5) : 1009-1022. doi: 10.3934/dcdss.2015.8.1009
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