Aspects Concerning Validation of Theoretical Solution of Generalised Ladder Problem
Abstract
1. Introduction
1.1. The Ladder Problem
1.2. Obtaining the Equation of Motion of the Classical Model
1.3. Numerical Solution of the Classical Model
2. Material and Method
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- The friction between the rod and the walls cannot be neglected in the actual model;
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- The actual rod has a certain cross-section, and the contact between the rod and the wall occurs along its edge;
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- The difficulty in ensuring the plane-parallel motion of the rod in the vertical plane.
2.1. Dynamical Analysis Using Dynamic Simulation Software
2.2. Analytical Solution of the Proposed Model
3. Results and Discussions
- Deduction of the nonlinear differential equation of motion;
- The numerical integration of the equation of motion for the specified initial conditions;
- Finding the expressions of the normal reactions from the two sphere–wall contacts;
- Finding the time when the vertical contact disrupts, imposing the condition of cancelled reaction from the vertical wall, the instant that corresponds to the transition from a 1DOF system into a 2DOF system;
- The design and construction of a device used for experimental validation of the analytical solutions;
- The numerical simulation of the motion of the system using a software gave results in disagreement with the physical reality.
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Launching | Frame Number [−] | Displacement [mm] |
---|---|---|
set 1 | 3488 | 232 |
3502 | 225 | |
3506 | 220 | |
3515 | 210 | |
3521 | 200 | |
3526 | 190 | |
3530 | 180 | |
3533 | 173 | |
3536 | 162 | |
3539 | 152 | |
3542 | 141 | |
3544 | 133 | |
3547 | 120 | |
3550 | 107 | |
set 2 | 4535 | 230 |
4552 | 220 | |
4562 | 210 | |
4569 | 200 | |
4574 | 190 | |
4579 | 180 | |
4582 | 170 | |
4586 | 160 | |
4588 | 150 | |
4591 | 140 | |
4594 | 130 | |
4596 | 120 | |
4599 | 108 |
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Lupascu, C.; Alaci, S.; Ciornei, F.-C.; Romanu, I.-C.; Cerlinca, D.-A.; Bujoreanu, C. Aspects Concerning Validation of Theoretical Solution of Generalised Ladder Problem. Modelling 2025, 6, 28. https://doi.org/10.3390/modelling6020028
Lupascu C, Alaci S, Ciornei F-C, Romanu I-C, Cerlinca D-A, Bujoreanu C. Aspects Concerning Validation of Theoretical Solution of Generalised Ladder Problem. Modelling. 2025; 6(2):28. https://doi.org/10.3390/modelling6020028
Chicago/Turabian StyleLupascu, Costica, Stelian Alaci, Florina-Carmen Ciornei, Ionut-Cristian Romanu, Delia-Aurora Cerlinca, and Carmen Bujoreanu. 2025. "Aspects Concerning Validation of Theoretical Solution of Generalised Ladder Problem" Modelling 6, no. 2: 28. https://doi.org/10.3390/modelling6020028
APA StyleLupascu, C., Alaci, S., Ciornei, F.-C., Romanu, I.-C., Cerlinca, D.-A., & Bujoreanu, C. (2025). Aspects Concerning Validation of Theoretical Solution of Generalised Ladder Problem. Modelling, 6(2), 28. https://doi.org/10.3390/modelling6020028