Abstract
We analyse a model of a swing where the swing is regarded as a pendulum with a variable length under the influence of friction. Related to the optimal control of the swing, we discuss the various pumping manners and the effects of their properties such as the pumping frequency, pumping phase and pumping amplitude. The optimal pumping manner can be the step pumping, where sitting (standing) occurs when the swing goes from the highest (lowest) position to the lowest (highest) position with as large a pumping amplitude as possible.
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