Geodesic
A simple trolley-like model in the presence of a nonlinear friction and a bounded fuel expenditure
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 33 (2013) no. 2, pp. 135-147.

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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.
Keywords: optimal control problem, Pontryagin Maximum Principle, extremals, singular arcs 
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Dmitruk, Andrei; Samylovskiy, Ivan. A simple trolley-like model in the presence of a nonlinear friction and a bounded fuel expenditure. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 33 (2013) no. 2, pp. 135-147. http://geodesic.mathdoc.fr/item/DMDICO_2013_33_2_a1/

[1] R.H. Goddard, A method on reaching extreme altitudes Smitsonian Miscellaneous Collection 71 (1919) 82 pages

[2] J.F. Bonnans, P. Martinon and E. Trelat, Singular arcs in the generalized Goddard's Problem, JOTA 139 (2008) 439-461. doi: 10.1007/s10957-008-9387-1

[3] P. Martinon, F. Bonnans, J. Laurent-Varin and E. Trelat, Numerical study of optimal trajectories with singular arcs for an Ariane 5 launcher, J. Guidance, Control, and Dynamics 32 (2009) 51-55. doi: 10.2514/1.37387

[4] C. Ponssard, K. Graichen, N. Petit and J. Laurent-Varin, Ascent optimization for a heavy space launcher, Proceedings of the European Control Conference 2009, Budapest, Hungary (2009) 3033-3038.