The surface of non-linear rotation
The paper considers a geometric scheme, a mathematical model and an algorithm for shaping a non-linear rotation surface. It is known that in Euclidean geometry and mechanics the transformation of rotation is linear, while distance and angle are its invariants. The authors proposed a geometric sch...
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| Format: | Article |
| Language: | English |
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Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education
2023-11-01
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| Series: | Омский научный вестник |
| Subjects: | |
| Online Access: | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2023/%E2%84%964%20(188)%20(%D0%9E%D0%9D%D0%92)/5-12%20%D0%9F%D0%B0%D0%BD%D1%87%D1%83%D0%BA%20%D0%9A.%20%D0%9B.,%20%D0%9C%D1%8F%D1%81%D0%BE%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%20%D0%A2.%20%D0%9C..pdf |
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| _version_ | 1832563524850679808 |
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| author | K. L. Panchuk T. M. Myasoyedova |
| author_facet | K. L. Panchuk T. M. Myasoyedova |
| author_sort | K. L. Panchuk |
| collection | DOAJ |
| description | The paper considers a geometric scheme, a mathematical model and an algorithm
for shaping a non-linear rotation surface. It is known that in Euclidean geometry
and mechanics the transformation of rotation is linear, while distance and angle are
its invariants. The authors proposed a geometric scheme of non-linear rotation, in
which the axis of rotation is a smooth spatial curve and the object of rotation is a
smooth line. Several propositions, a lemma and a theorem are proved, which allow
one to form the initial data in the problem of nonlinear rotation, the solution of
which is the parametric equations of smooth surfaces. The research results make
it possible to expand the variety of cyclic surfaces in the existing classification of
analytic surfaces. They can also be useful in the creation of CAD, which provides for
the design of surface forms of products for mechanical engineering, construction,
architecture and other practical areas based on cyclic surfaces. |
| format | Article |
| id | doaj-art-d212420ad66d409d9fb1ccb95e6cbb45 |
| institution | Kabale University |
| issn | 1813-8225 2541-7541 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Omsk State Technical University, Federal State Autonoumos Educational Institution of Higher Education |
| record_format | Article |
| series | Омский научный вестник |
| spelling | doaj-art-d212420ad66d409d9fb1ccb95e6cbb452025-02-03T01:14:11ZengOmsk State Technical University, Federal State Autonoumos Educational Institution of Higher EducationОмский научный вестник1813-82252541-75412023-11-014 (188)51210.25206/1813-8225-2023-188-5-12The surface of non-linear rotationK. L. Panchuk0https://orcid.org/0000-0001-9302-8560T. M. Myasoyedova1https://orcid.org/0000-0002-9641-9417Omsk State Technical UniversityOmsk State Technical UniversityThe paper considers a geometric scheme, a mathematical model and an algorithm for shaping a non-linear rotation surface. It is known that in Euclidean geometry and mechanics the transformation of rotation is linear, while distance and angle are its invariants. The authors proposed a geometric scheme of non-linear rotation, in which the axis of rotation is a smooth spatial curve and the object of rotation is a smooth line. Several propositions, a lemma and a theorem are proved, which allow one to form the initial data in the problem of nonlinear rotation, the solution of which is the parametric equations of smooth surfaces. The research results make it possible to expand the variety of cyclic surfaces in the existing classification of analytic surfaces. They can also be useful in the creation of CAD, which provides for the design of surface forms of products for mechanical engineering, construction, architecture and other practical areas based on cyclic surfaces.https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2023/%E2%84%964%20(188)%20(%D0%9E%D0%9D%D0%92)/5-12%20%D0%9F%D0%B0%D0%BD%D1%87%D1%83%D0%BA%20%D0%9A.%20%D0%9B.,%20%D0%9C%D1%8F%D1%81%D0%BE%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%20%D0%A2.%20%D0%9C..pdfsmooth curvemovable trihedronnon-linear rotation surfaceshaping algorithmcyclic surface |
| spellingShingle | K. L. Panchuk T. M. Myasoyedova The surface of non-linear rotation Омский научный вестник smooth curve movable trihedron non-linear rotation surface shaping algorithm cyclic surface |
| title | The surface of non-linear rotation |
| title_full | The surface of non-linear rotation |
| title_fullStr | The surface of non-linear rotation |
| title_full_unstemmed | The surface of non-linear rotation |
| title_short | The surface of non-linear rotation |
| title_sort | surface of non linear rotation |
| topic | smooth curve movable trihedron non-linear rotation surface shaping algorithm cyclic surface |
| url | https://www.omgtu.ru/general_information/media_omgtu/journal_of_omsk_research_journal/files/arhiv/2023/%E2%84%964%20(188)%20(%D0%9E%D0%9D%D0%92)/5-12%20%D0%9F%D0%B0%D0%BD%D1%87%D1%83%D0%BA%20%D0%9A.%20%D0%9B.,%20%D0%9C%D1%8F%D1%81%D0%BE%D0%B5%D0%B4%D0%BE%D0%B2%D0%B0%20%D0%A2.%20%D0%9C..pdf |
| work_keys_str_mv | AT klpanchuk thesurfaceofnonlinearrotation AT tmmyasoyedova thesurfaceofnonlinearrotation AT klpanchuk surfaceofnonlinearrotation AT tmmyasoyedova surfaceofnonlinearrotation |