Abstract
The problem of finding a periodic motion of generalized Atwood’s machine in which the pulley of a finite radius is replaced by two small pulleys and one of the objects may oscillate in the vertical plane is discussed. Using symbolic computations, the equations of motion are derived and their periodic solutions in the form of power series in a small parameter in the case of small oscillations are obtained. It is shown that if the difference of the objects' masses is small, then the system has a dynamic equilibrium state in which the oscillating object behaves like a pendulum the length of which performs small oscillations. In this case, the frequency resonance \(2:1\) is observed; i.e., the pendulum length oscillation frequency is twice as large as the oscillation frequency of the angular variable. The comparison of the analytical results with the numerical solutions to the equations of motion confirms the validity of the analytical computations. All computations are performed using the computer algebra system Wolfram Mathematica.
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Translated by A. Klimontovich
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Prokopenya, A.N. Construction of a Periodic Solution to the Equations of Motion of Generalized Atwood’s Machine using Computer Algebra. Program Comput Soft 46, 120–125 (2020). https://doi.org/10.1134/S0361768820020085
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DOI: https://doi.org/10.1134/S0361768820020085