Abstract
A simple pendulum is considered as a swing model. The distance between the suspension point of the swing and the center of mass of the person standing on it acts as a limited control action, and the swing with a person on it is a system with one degree of freedom. In the form of feedback, an optimal control is constructed, under which the most rapid increase in the oscillation amplitude occurs. If the coefficient of viscous friction at the suspension point of the swing is large enough, then under this control the swing asymptotically enters the steady-state oscillation mode with a constant amplitude. If the coefficient of friction is rather small, then the oscillations of the swing turn into rotation around the suspension point. A more realistic swing model is also considered with two degrees of freedom. In this model, the control is a force that moves the center of mass of a person along the swing.
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Klimina, L.A., Formalskii, A.M. On the Optimal Swinging of a Swing by a Person Standing on It. J. Comput. Syst. Sci. Int. 61, 944–953 (2022). https://doi.org/10.1134/S1064230722060119
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DOI: https://doi.org/10.1134/S1064230722060119