https://doi.org/10.1140/epjb/s10051-022-00435-5
Regular Article - Statistical and Nonlinear Physics
Regular and chaotic motion of two bodies swinging on a rod
1
School of Physics, Free University of Tbilisi, David Aghmashenebeli Alley, 0159, Tbilisi, Georgia
2
Department of Physics, Ivane Javakhishvili Tbilisi State University, 3 Chavchavadze, 0128, Tbilisi, Georgia
a
lazare.osmanov1521@gmail.com
Received:
5
April
2022
Accepted:
10
October
2022
Published online:
7
November
2022
We investigate regular and chaotic dynamics of two bodies swinging on a rod, which differs from all the other mechanical analogies: depending on initial conditions, its oscillation could end very quickly and the reason is not a drag force or energy loss. We use various tools to analyze motion, such as Poincaré section for quasi-periodic and chaotic cases. We calculate Lyapunov characteristic exponent by different methods including Finite Time Lyapunov Exponent analysis. Our calculations show that the maximal Lyapunov exponent is always positive except in the marginal cases when one observes quasi-periodic oscillations.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
