PLAYING WITH A CHAIN OR PHYSICAL AND MATHEMATICAL INFORMATICS
The article describes an educational laboratory work within the framework of interdisciplinary connec- tions at the intersection of informatics, mathematics and physics: the study of the sagging of a closed chain with different support points. A technology of computer processing of photos and videos...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | Russian |
| Published: |
The Fund for Promotion of Internet media, IT education, human development «League Internet Media»
2018-06-01
|
| Series: | Современные информационные технологии и IT-образование |
| Subjects: | |
| Online Access: | http://sitito.cs.msu.ru/index.php/SITITO/article/view/390 |
| _version_ | 1831553977194381312 |
|---|---|
| author | Valery F. Ochkov Massimiliano Nori |
| author_facet | Valery F. Ochkov Massimiliano Nori |
| author_sort | Valery F. Ochkov |
| collection | DOAJ |
| description | The article describes an educational laboratory work within the framework of interdisciplinary connec- tions at the intersection of informatics, mathematics and physics: the study of the sagging of a closed chain with different support points. A technology of computer processing of photos and videos of a physical ex- periment with the subsequent processing of the media files on the computer is illustrated. We present the π chain number (1.258... − the optimal ratio of the chain length to the distance between its attachment points) and its relation to the previously unexplored problem of the shape of the sag of a closed chain hanging on two nails. The analytic expression for this constant was first found. A new physical and math- ematical constant is found − the critical angle of the sagging of a closed chain on the “hangers”. The prob- lem of the sagging of a closed chain on a cone is detailed. The applicability of the computer tool “optimiza- tion with constraints” for solving problems of theoretical mechanics is investigated. Three main tools of mathematical computer tools are described: numerical mathematics, symbolic mathematics and graphics. The importance of using units of measurement when solving physical problems on a computer is empha- sized. The problem of publishing mathematical formulas in articles and books is discussed. |
| first_indexed | 2024-12-17T03:54:22Z |
| format | Article |
| id | doaj.art-a296ffba388a43068dc5bf417b649edb |
| institution | Directory Open Access Journal |
| issn | 2411-1473 |
| language | Russian |
| last_indexed | 2024-12-17T03:54:22Z |
| publishDate | 2018-06-01 |
| publisher | The Fund for Promotion of Internet media, IT education, human development «League Internet Media» |
| record_format | Article |
| series | Современные информационные технологии и IT-образование |
| spelling | doaj.art-a296ffba388a43068dc5bf417b649edb2022-12-21T22:04:40ZrusThe Fund for Promotion of Internet media, IT education, human development «League Internet Media»Современные информационные технологии и IT-образование2411-14732018-06-0114233334310.25559/SITITO.14.201802.333-343PLAYING WITH A CHAIN OR PHYSICAL AND MATHEMATICAL INFORMATICSValery F. Ochkov0Massimiliano Nori1National Research University Moscow Power Engineering Institute, Moscow, RussiaSaipem S.p.A., San Donato Milanese, ItalyThe article describes an educational laboratory work within the framework of interdisciplinary connec- tions at the intersection of informatics, mathematics and physics: the study of the sagging of a closed chain with different support points. A technology of computer processing of photos and videos of a physical ex- periment with the subsequent processing of the media files on the computer is illustrated. We present the π chain number (1.258... − the optimal ratio of the chain length to the distance between its attachment points) and its relation to the previously unexplored problem of the shape of the sag of a closed chain hanging on two nails. The analytic expression for this constant was first found. A new physical and math- ematical constant is found − the critical angle of the sagging of a closed chain on the “hangers”. The prob- lem of the sagging of a closed chain on a cone is detailed. The applicability of the computer tool “optimiza- tion with constraints” for solving problems of theoretical mechanics is investigated. Three main tools of mathematical computer tools are described: numerical mathematics, symbolic mathematics and graphics. The importance of using units of measurement when solving physical problems on a computer is empha- sized. The problem of publishing mathematical formulas in articles and books is discussed.http://sitito.cs.msu.ru/index.php/SITITO/article/view/390Theoretical mechanicssagging chainchain functionderivativeintegralpotential energykinetic energyLagrange-Dirichlet principleNewton’s lawconstrained optimizationsystem of algebraic equationscomputer graphicsanimationMathcad |
| spellingShingle | Valery F. Ochkov Massimiliano Nori PLAYING WITH A CHAIN OR PHYSICAL AND MATHEMATICAL INFORMATICS Современные информационные технологии и IT-образование Theoretical mechanics sagging chain chain function derivative integral potential energy kinetic energy Lagrange-Dirichlet principle Newton’s law constrained optimization system of algebraic equations computer graphics animation Mathcad |
| title | PLAYING WITH A CHAIN OR PHYSICAL AND MATHEMATICAL INFORMATICS |
| title_full | PLAYING WITH A CHAIN OR PHYSICAL AND MATHEMATICAL INFORMATICS |
| title_fullStr | PLAYING WITH A CHAIN OR PHYSICAL AND MATHEMATICAL INFORMATICS |
| title_full_unstemmed | PLAYING WITH A CHAIN OR PHYSICAL AND MATHEMATICAL INFORMATICS |
| title_short | PLAYING WITH A CHAIN OR PHYSICAL AND MATHEMATICAL INFORMATICS |
| title_sort | playing with a chain or physical and mathematical informatics |
| topic | Theoretical mechanics sagging chain chain function derivative integral potential energy kinetic energy Lagrange-Dirichlet principle Newton’s law constrained optimization system of algebraic equations computer graphics animation Mathcad |
| url | http://sitito.cs.msu.ru/index.php/SITITO/article/view/390 |
| work_keys_str_mv | AT valeryfochkov playingwithachainorphysicalandmathematicalinformatics AT massimilianonori playingwithachainorphysicalandmathematicalinformatics |