A Novel Analysis of the Smooth Curve with Constant Width Based on a Time Delay System

A Novel Analysis of the Smooth Curve with Constant Width Based on a Time Delay System

In this paper, we analyze the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>∞</mo></msup></semantics></math></inline-formula> smooth curve of...

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Bibliographic Details
Main Authors: Teng Fu, Yusheng Zhou
Format: Article
Language:English
Published: MDPI AG 2021-05-01
Series:Mathematics
Subjects:
smooth curve of constant width
characteristic equation
time delay system
<i>C</i><sup>∞</sup> smooth
Online Access:https://www.mdpi.com/2227-7390/9/10/1131
Description
Summary:In this paper, we analyze the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>C</mi><mo>∞</mo></msup></semantics></math></inline-formula> smooth curve of constant width using the characteristic equation of a time delay system. We prove that a closed convex curve must be a circle if it is still a smooth curve of constant width after taking any number of derivatives. Finally, the simulation results are presented for analyzing the influence of derivative orders on a smooth non-circular curve of constant width.
ISSN:2227-7390

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