Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 12, 17 November 2023
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Research on the bidirectional sliding phenomena of a toppling rod under frictional situations
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Abstract
In this work, we investigated the phenomenon of spontaneous bidirectional sliding on a toppling rod under a frictional situation. We explained the reasons for sliding is the friction force from the table is not sufficient to support the horizontal acceleration of the mass center when toppling, so the rod itself has to obtain a horizontal acceleration and apply the inertia force to play the role of supporting the acceleration of the mass center. This phenomenon and converted the question into a mathematical model. We pick the contacting point between the rod and the horizontal surface as the reference point for our computing of physical quantity, therefore the torque caused by friction and normal force can be ignored. With this model, we finished the theoretical analysis of the effects of varying static friction and dynamic friction coefficients on the phenomenon, with computer simulations verified.
Keywords
classical mechanics, rotation, rigid body, friction, mathematical modeling
References
1. Louis N Hand and Janet D Finch. Analytical Mechanics. en. Cambridge, England: Cambridge University Press, Nov. 1998.
2. Andy Ruina and Rudra Pratap. Introduction to Statics and Dynamics. Oxford University Press, 2015.
3. Raymond Serway. Physics for Scientists and Engineers : With modern physics. 2nd ed. Saunders College Publishing, 1986.
4. John R Taylor. Classical Mechanics. en. Sausalito, CA: University Science Books, Sept. 2004.
5. Carl Gustav Jacob Jacobi. Cambridge Library Collection - Mathematics: Fundamenta nova theoriae functionum ellipticarum. la. Cambridge, England: Cambridge University Press, Nov. 2012.
6. Angel de la Fuente. Mathematical methods and models for economists. Cambridge, England: Cambridge University Press, Jan. 2000.
7. Wolfram Research, ContourPlot, Wolfram. 1988 https://reference.wolfram.com/language/ref/ ContourPlot.html
8. PyTorch Contributors, Hardtanh. 2023 https://pytorch.org/docs/stable/generated/torch.nn. Hardtanh.html
9. Mechanical Engineering Department: Tribology Introduction. 2016 http://mechanicalemax. blogspot.com/2016/03/tribology-introduction.html
10. Friction Factors – Coefficients of Friction. 2015 https://www.roymech.co.uk/Useful_Tables/ Tribology/co_of_frict.htm
Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of the 2023 International Conference on Mathematical Physics and Computational Simulation
- ISBN (Print)
- 978-1-83558-135-3
- ISBN (Online)
- 978-1-83558-136-0
- Published Date
- 17 November 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/12/20230438
- Copyright
- 17 November 2023
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited