From linear to non-linear/chaotic pendulum: a computational study
In this work, we have used computational techniques to examine how the dynamics of a simple pendulum change from linear to non-linear and chaotic. The graph of phase space, angular displacement versus time, and angular velocity versus time are thoroughly examined in our analysis. A significant shif...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Department of Physics, Mahendra Morang Adarsh Multiple Campus, Tribhuvan University
2025-05-01
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| Series: | Bibechana |
| Subjects: | |
| Online Access: | https://www.nepjol.info/index.php/BIBECHANA/article/view/72570 |
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| Summary: | In this work, we have used computational techniques to examine how the dynamics of a simple pendulum change from linear to non-linear and chaotic. The graph of phase space, angular displacement versus time, and angular velocity versus time are thoroughly examined in our analysis. A significant shift is seen in these representations, particularly in the graph of angular displacement versus time and angular velocity versus time. As the non-linearity is enhanced, we see a progressive movement from circular to oval shapes in phase space. In damped and forced pendulum scenarios, similar patterns are observed. In these cases, the graphs display a sinusoidal pattern with a diminishing amplitude with time. Surprisingly, in the phase space of the damped pendulum, a spiral type of graph is observed, demonstrating the intricate relationship between damping effects and nonlinearity. This research emphasizes the separatrix’s function as a crucial cutoff point where the motion of the pendulum changes from linear to chaotic.
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| ISSN: | 2091-0762 2382-5340 |