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Analysis of the rolling motion of loaded hoops
Thesis (PhD (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2008.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : University of Stellenbosch
2008
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| _version_ | 1867613908592754688 |
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| access_status_str | Open Access |
| author | Theron, Willem F. D. |
| author2 | Maritz, M. F. |
| author_browse | Maritz, M. F. Theron, Willem F. D. |
| author_facet | Maritz, M. F. Theron, Willem F. D. |
| author_sort | Theron, Willem F. D. |
| collection | Thesis |
| dc_rights_str_mv | University of Stellenbosch |
| description | Thesis (PhD (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2008. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/1206 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:43:37.288Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2008 |
| publishDateRange | 2008 |
| publishDateSort | 2008 |
| publisher | Stellenbosch : University of Stellenbosch |
| publisherStr | Stellenbosch : University of Stellenbosch |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/1206 Analysis of the rolling motion of loaded hoops Theron, Willem F. D. Maritz, M. F. University of Stellenbosch. Faculty of Science. Dept. of Mathematical Sciences. Applied Mathematics. Classical mechanics Rolling motion Hopping hoops Loaded wheels Dynamics Equations of motion Lagrange equations Dissertations -- Applied mathematics Theses -- Applied mathematics Thesis (PhD (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2008. This dissertation contains a detailed report on the results of a research project on the behaviour of a dynamical system consisting of a hoop to which a heavy particle is fixed at the rim. This loaded hoop rolls on a rough surface while remaining in the vertical plane. The motion of the hoop consists of various, possibly alternating, phases consisting of rolling without slipping, spinning or skidding motion and in some cases ends by hopping off the surface. A general mathematical model is developed, consisting of a system of second order ordinary differential equations, one for each of the three degrees of freedom. Analytic solutions are obtained in some cases; otherwise numerical solutions are used. Three specific applications of the general model are dealt with. In the first application the problem of massless hoops is investigated. The main emphasis is on the somewhat controversial question of what happens after the normal reaction becomes zero in a position where the particle is still moving downwards. A new result shows that the hoop can continue to move horizontally in a motion defined as skimming. The second application deals with rigid hoops and a large number of detailed results are presented. Classification schemes for the different types of behaviour are introduced and summarised in the form of phase diagrams. Some emphasis is placed on the rather amazing number of different patterns of motion that can be obtained by varying the parameters. In the third application two elastic models are analysed, with the primary purpose of explaining one aspect of the reported behaviour of experimental hoops, namely hopping while the particle is moving downwards. A chapter on experimental models rounds off the project. Doctoral 2008-06-23T12:47:27Z 2010-06-01T08:15:02Z 2008-06-23T12:47:27Z 2010-06-01T08:15:02Z 2008-03 Thesis http://hdl.handle.net/10019.1/1206 en University of Stellenbosch application/pdf Stellenbosch : University of Stellenbosch |
| spellingShingle | Classical mechanics Rolling motion Hopping hoops Loaded wheels Dynamics Equations of motion Lagrange equations Dissertations -- Applied mathematics Theses -- Applied mathematics Theron, Willem F. D. Analysis of the rolling motion of loaded hoops |
| title | Analysis of the rolling motion of loaded hoops |
| title_full | Analysis of the rolling motion of loaded hoops |
| title_fullStr | Analysis of the rolling motion of loaded hoops |
| title_full_unstemmed | Analysis of the rolling motion of loaded hoops |
| title_short | Analysis of the rolling motion of loaded hoops |
| title_sort | analysis of the rolling motion of loaded hoops |
| topic | Classical mechanics Rolling motion Hopping hoops Loaded wheels Dynamics Equations of motion Lagrange equations Dissertations -- Applied mathematics Theses -- Applied mathematics |
| url | http://hdl.handle.net/10019.1/1206 |
| work_keys_str_mv | AT theronwillemfd analysisoftherollingmotionofloadedhoops |