On the development of Pontryagin's Maximum Principle in the works of A. Ya. Dubovitskii and A. A. Milyutin
Jacobi type conditions for singular extremals
A simple trolley-like model in the presence of a nonlinear friction and a bounded fuel expenditure
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.
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