Mathematical Description for a Particular Case of Ellipse Focus Quasi-Rotation Around an Elliptical Axis

I. V. Antonova; E. Solomonova; Nina S. Kadykova

doi:10.12737/2308-4898-2021-9-1-39-45

UDC 51

MATHEMATICAL DESCRIPTION FOR A PARTICULAR CASE OF ELLIPSE FOCUS QUASI-ROTATION AROUND AN ELLIPTICAL AXIS Mathematical Description for a Particular Case of Ellipse Focus Quasi-Rotation Around an Elliptical Axis

АА Аа

Published in Geometry & Graphics · Volume 9, Issue 1 · Pages 39–45 · Rubric: Scientific problems of geometry

DOI: https://doi.org/10.12737/2308-4898-2021-9-1-39-45

Received: 05.07.2021 Accepted: 24.03.2024 Language of publication: ru-RU

Authors

I. V. Antonova

E. Solomonova

Nina S. Kadykova

I. V. Antonova

Academic degree: candidate of pedagogical sciences

MIREA – Russian Technological University Associate Professor · kafedra vysshey i prikladnoy matematiki · Russian Federation

E. Solomonova

MIREA – Russian Technological University Senior Lecturer · Institute of Fine Chemical Technologies named after M.V. Lomonosov · Russian Federation

Nina S. Kadykova

Academic degree: candidate of technical sciences

Science rang: docent

MIREA — Russian Technological University Associate Professor · Department of Engineering Graphics · Russian Federation · Москва

ABSTRACT

In this paper is provided mathematical analysis related to a particular case for a point quasi-rotation around a curve of an elliptical axis. The research complements the previous works in this direction. Has been considered a special case, in which the quasi-rotation correspondence is applied to a point located at the elliptical axis’s focus. This case is special, since the quasi-rotation center search is not invariant and does not lead to determination of four quasi-rotation centers, as in the general case. A constructive approach to the rotation center search shows that any point lying on the elliptical axis can be the quasi-rotation center. This feature leads to the fact that instead of four circles, the quasi-rotation of a point lying in the elliptical axis’s focus leads to the formation of an infinite number of circle families, which together form a channel surface. The resulting surface is a Dupin cyclide, whose throat circle has a zero radius and coincides with the original generating point. While analyzing are considered all cases of the rotation center location. Geometric constructions have been performed based on previously described methods of rotation around flat geometric objects’ curvilinear axes. For the study, the mathematical relationship between the coordinates of the initial set point, the axis curve equation and the motion trajectory equation of this point around the axis curve, described in earlier papers on this topic, is used. In the proposed paper has been provided the derivation of the motion trajectory equation for a point around the elliptic axis’s curve.

KEYWORDS

ellipse; focus; rotation center; rotation trajectory; parametric equations

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JATS XML

Zamestitel' glavnogo redaktora, chlen redsoveta

Vladimir Vyshnyepolskiy

Glavnyy redaktor

A. A. Ishchenko

Vypuskayuschiy redaktor

Dar'ya Sklyankina

501@infra-m.ru

Deputy editor-in-chief, member of the editorial Board

N. Sal'kov

nikolaysalkov@mail.ru

GOST

Antonova I. V., Solomonova E. V., Kadykova N. S. Mathematical Description for a Particular Case of Ellipse Focus Quasi-Rotation Around an Elliptical Axis // Geometry & Graphics. 2021. no. 1. pp. 39-45. DOI: https://doi.org/10.12737/2308-4898-2021-9-1-39-45. (Date of access 12.11.2026).

MLA

I. V. Antonova, Solomonova E. V., Kadykova N. S.. "Mathematical Description for a Particular Case of Ellipse Focus Quasi-Rotation Around an Elliptical Axis." Geometry & Graphics 9.1 (2021): 39-45. DOI: https://doi.org/10.12737/2308-4898-2021-9-1-39-45.

APA

Antonova I. V., Solomonova E. V., Kadykova N. S. (2021). Mathematical Description for a Particular Case of Ellipse Focus Quasi-Rotation Around an Elliptical Axis. Geometry & Graphics, 9(1), 39-45. https://doi.org/10.12737/2308-4898-2021-9-1-39-45

Chicago

I. V. Antonova, Solomonova E. V., Kadykova N. S.. "Mathematical Description for a Particular Case of Ellipse Focus Quasi-Rotation Around an Elliptical Axis." Geometry & Graphics 9, no. 1 (2021): 39-45. https://doi.org/10.12737/2308-4898-2021-9-1-39-45.

WIKI

{{cite journal | author = Antonova I. V., Solomonova E. V., Kadykova N. S. | title = Mathematical Description for a Particular Case of Ellipse Focus Quasi-Rotation Around an Elliptical Axis | journal = Geometry & Graphics | year = 2021 | volume = 9 | issue = 1 | pages = 39-45 | doi = 10.12737/2308-4898-2021-9-1-39-45 }}

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MATHEMATICAL DESCRIPTION FOR A PARTICULAR CASE OF ELLIPSE FOCUS QUASI-ROTATION AROUND AN ELLIPTICAL AXIS Mathematical Description for a Particular Case of Ellipse Focus Quasi-Rotation Around an Elliptical Axis

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