The mathematics and mechanics of tug of war
In this paper, we propose a mechanical model for a game of tug of war (rope pulling). We focus on a game opposing two players, modelling each player’s body as a structure composed of straight rods that can be actuated in three different ways to generate a pulling force. We first examine the static p...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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SAGE Publications
2024
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| _version_ | 1811140411679309824 |
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| author | Moulton, D Oliveri, H |
| author_facet | Moulton, D Oliveri, H |
| author_sort | Moulton, D |
| collection | OXFORD |
| description | In this paper, we propose a mechanical model for a game of tug of war (rope pulling). We focus on a game opposing two players, modelling each player’s body as a structure composed of straight rods that can be actuated in three different ways to generate a pulling force. We first examine the static problem of two opponents being in a deadlock configuration of mechanical equilibrium; here we show that this situation is essentially governed by the ratio of masses of the players, with the heavier player having a strong advantage. We then turn to the dynamic problem and model the response of the system to an abrupt change in activation by one of the players. In this case, the system exhibits a nontrivial response; in particular, we compare a sudden pulling and a sudden “letting up,” and demonstrate the existence of regimes in which the lighter player can momentarily take the advantage. |
| first_indexed | 2024-03-07T08:19:39Z |
| format | Journal article |
| id | oxford-uuid:151b9836-dfb6-4ce0-a1ab-294af6462b33 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:21:34Z |
| publishDate | 2024 |
| publisher | SAGE Publications |
| record_format | dspace |
| spelling | oxford-uuid:151b9836-dfb6-4ce0-a1ab-294af6462b332024-08-19T11:22:31ZThe mathematics and mechanics of tug of warJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:151b9836-dfb6-4ce0-a1ab-294af6462b33EnglishSymplectic ElementsSAGE Publications2024Moulton, DOliveri, HIn this paper, we propose a mechanical model for a game of tug of war (rope pulling). We focus on a game opposing two players, modelling each player’s body as a structure composed of straight rods that can be actuated in three different ways to generate a pulling force. We first examine the static problem of two opponents being in a deadlock configuration of mechanical equilibrium; here we show that this situation is essentially governed by the ratio of masses of the players, with the heavier player having a strong advantage. We then turn to the dynamic problem and model the response of the system to an abrupt change in activation by one of the players. In this case, the system exhibits a nontrivial response; in particular, we compare a sudden pulling and a sudden “letting up,” and demonstrate the existence of regimes in which the lighter player can momentarily take the advantage. |
| spellingShingle | Moulton, D Oliveri, H The mathematics and mechanics of tug of war |
| title | The mathematics and mechanics of tug of war |
| title_full | The mathematics and mechanics of tug of war |
| title_fullStr | The mathematics and mechanics of tug of war |
| title_full_unstemmed | The mathematics and mechanics of tug of war |
| title_short | The mathematics and mechanics of tug of war |
| title_sort | mathematics and mechanics of tug of war |
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