Theoretical and Computational Analysis of the Falling Ladder Problem
Abstract A comprehensive study of the falling ladder problem is presented. The ladder may fall naturally under the influence of gravity alone and at some point lose its contact with the wall or it may be kept in contact with the wall by a physical constraint. Several scenarios about the way the poi...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer Singapore
2021
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| Online Access: | https://hdl.handle.net/1721.1/131433 |
| _version_ | 1826194213984796672 |
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| author | Ghorashi, Ali Ghorashi, Mehrdaad |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Ghorashi, Ali Ghorashi, Mehrdaad |
| author_sort | Ghorashi, Ali |
| collection | MIT |
| description | Abstract
A comprehensive study of the falling ladder problem is presented. The ladder may fall naturally under the influence of gravity alone and at some point lose its contact with the wall or it may be kept in contact with the wall by a physical constraint. Several scenarios about the way the point of contact with the floor is moved are also considered. While solutions for the case of moving this point at constant velocity exist, generating such a motion requires implementation of an actuator. Here, the more general case of moving this point by an actuator at constant acceleration is presented and the required varying actuator force is calculated. Furthermore, computer simulations using MATLAB and the motion analysis tool of SolidWorks are generated to verify the theoretical results. Computer simulations are also used to display a comprehensive set of the findings. The theoretical results given in this paper can be used as benchmarks (in applications like robotics) for generating more realistic computer simulations and animations where elements behaving like the ladder discussed here are part of a mechanism. |
| first_indexed | 2024-09-23T09:52:40Z |
| format | Article |
| id | mit-1721.1/131433 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:52:40Z |
| publishDate | 2021 |
| publisher | Springer Singapore |
| record_format | dspace |
| spelling | mit-1721.1/1314332023-02-17T19:13:19Z Theoretical and Computational Analysis of the Falling Ladder Problem Ghorashi, Ali Ghorashi, Mehrdaad Massachusetts Institute of Technology. Department of Physics Abstract A comprehensive study of the falling ladder problem is presented. The ladder may fall naturally under the influence of gravity alone and at some point lose its contact with the wall or it may be kept in contact with the wall by a physical constraint. Several scenarios about the way the point of contact with the floor is moved are also considered. While solutions for the case of moving this point at constant velocity exist, generating such a motion requires implementation of an actuator. Here, the more general case of moving this point by an actuator at constant acceleration is presented and the required varying actuator force is calculated. Furthermore, computer simulations using MATLAB and the motion analysis tool of SolidWorks are generated to verify the theoretical results. Computer simulations are also used to display a comprehensive set of the findings. The theoretical results given in this paper can be used as benchmarks (in applications like robotics) for generating more realistic computer simulations and animations where elements behaving like the ladder discussed here are part of a mechanism. 2021-09-20T17:17:03Z 2021-09-20T17:17:03Z 2019-09-07 2020-09-24T20:44:58Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/131433 SN Computer Science. 2019 Sep 07;1(1):20 en https://doi.org/10.1007/s42979-019-0019-7 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer Nature Singapore Pte Ltd application/pdf Springer Singapore Springer Singapore |
| spellingShingle | Ghorashi, Ali Ghorashi, Mehrdaad Theoretical and Computational Analysis of the Falling Ladder Problem |
| title | Theoretical and Computational Analysis of the Falling Ladder Problem |
| title_full | Theoretical and Computational Analysis of the Falling Ladder Problem |
| title_fullStr | Theoretical and Computational Analysis of the Falling Ladder Problem |
| title_full_unstemmed | Theoretical and Computational Analysis of the Falling Ladder Problem |
| title_short | Theoretical and Computational Analysis of the Falling Ladder Problem |
| title_sort | theoretical and computational analysis of the falling ladder problem |
| url | https://hdl.handle.net/1721.1/131433 |
| work_keys_str_mv | AT ghorashiali theoreticalandcomputationalanalysisofthefallingladderproblem AT ghorashimehrdaad theoreticalandcomputationalanalysisofthefallingladderproblem |