Geodesic
Optimization of the motion in a resistant medium of a body with a movable internal mass
Trudy Instituta matematiki i mehaniki, Dynamical systems: modeling, optimization, and control, Tome 12 (2006) no. 1, pp. 242-248 
F. L. Chernous'ko. Optimization of the motion in a resistant medium of a body with a movable internal mass. Trudy Instituta matematiki i mehaniki, Dynamical systems: modeling, optimization, and control, Tome 12 (2006) no. 1, pp. 242-248. http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a17/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The motion, in a resistant medium, of a system consisting of a rigid body and movable internal mass is considered. The external medium acts on the body by a force that piecewise linearly depends on its speed. The class of periodic motions of the internal mass for which the speed of this mass relative to the body is piecewise constant is studied. It is shown that, under certain conditions, the forward movement of the whole system in the medium is possible. The average speed of this movement over a period is determined. Optimal parameters of the motion of the internal mass for which the average speed of the system movement is maximal are found.

[1] Chernousko F. L., “O dvizhenii tela, soderzhaschego podvizhnuyu vnutrennyuyu massu”, Dokl. Akademii Nauk, 405:1 (2005), 56–60 | MR

[2] Chernousko F. L., “Optimal motion of a body controlled by internal masses”, Teoriya upravleniya i teoriya obobschennykh reshenii uravnenii Gamiltona–Yakobi, Trudy mezhdunarodnogo seminara. Tom 1 (22–26 iyunya 2005 g.), Ekaterinburg, 2006, 55–66

[3] Li H., Furuta K., Chernousko F. L., A pendulum-driven cart via internal force and static friction, Proceedings of International Conference “Physics and Control”, St. Petersburg, Russia, 15–17