On a curve and a system
1 Faculty of Education, Bayburt University, Bayburt, Turkey.
2 Faculty of Science and Arts, Manisa Celal Bayar University, Manisa, Turkey.
3 Faculty of Science and Arts, Manisa Celal Bayar University, Manisa, Turkey.
4 Faculty of Engineering and Natural Sciences, Bursa Technical University, Bursa, Turkey.
Research Article
GSC Advanced Research and Reviews, 2020, 05(03), 030-052.
Article DOI: 10.30574/gscarr.2020.5.3.0101
Publication history:
Received on 10 November 2020; revised on 17 November 2020; accepted on 19 November 2020
Abstract:
Curves of constant width, which have a very special place in many fields such as kinematics, engineering, art, cam design and geometry, are specially discussed under this title. In this study, a system of differential equations characterizing the curves of constant width is examined. This is the system of the first order homogenous differential equations with variable coefficients in the normal form. Approximate solutions of the system, by means of two different polynomial approaches, are calculated and error analysis is made. The obtained results are analyzed on a numerical sample and the best method of approach is determined. This system can also constitute a characterization for different types of curves according to different frames in different spaces. Therefore, this study is important not only for this curve type but also for the geometry of all curves that can be expressed in a similar system.
Keywords:
Curves of Constant Width; Hermite Matrix Collocation Method; Taylor Matrix Collocation Method; Frenet Frame; Reuleaux Triangle
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Copyright © 2020 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution Liscense 4.0
