A simple trolley-like model in the presence of a nonlinear friction and a bounded fuel expenditure
Andrei Dmitruk, Ivan Samylovskiy (2013)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We consider a problem of maximization of the distance traveled by a material point in the presence of a nonlinear friction under a bounded thrust and fuel expenditure. Using the maximum principle we obtain the form of optimal control and establish conditions under which it contains a singular subarc. This problem seems to be the simplest one having a mechanical sense in which singular subarcs appear in a nontrivial way.