Abstract
Linear motion of a mechanical system consisting of two bodies—a container and an inner body—is considered. The container is located in an external medium with resistance, and the inner body moves inside the container without the interaction with the external medium. Under certain conditions, the periodic motion of the inner body causes the system as a whole to move. The external medium acts on the container with a force that is proportional to its velocity with a resistance coefficient depending on the motion direction. Only the motions of the inner body with continuous relative velocity are studied. The optimal periodic motion of the inner body corresponding to the greatest period-averaged velocity of the system as a whole is constructed and analyzed.
Similar content being viewed by others
References
F. L. Chernous’ko, “On the Motion of a Body Containing a Movable Internal Mass,” Dokl. Phys. 50, 593–597 (2005).
F. L. Chernous’ko, “Analysis and Optimization of the Motion of a Body Controlled by means of a Movable Internal Mass,” J. Appl. Math. Mekh. 70, 819–842 (2006).
F. L. Chernous’ko, “Optimization of the Motion of a Body with Internal Movable Mass in Resistive Medium,” Tr. Inst. Mat. Mekh. UrO RAN 12(1), 242–248 (2006).
F. L. Chernous’ko, “The Optimal Periodic Motions of a Two-Mass System in a Resistant Medium,” J. Appl. Math. Mekh. 72, 116–125 (2008).
N. N. Bolotnik, T. Yu. Figurina, and F. L. Chernous’ko, “Optimal Control of the Rectilinear Motion of a Two-Body System in a Resistive Medium,” J. Appl. Math. Mekh. 76, 1–14 (2012).
N. N. Bolotnik and T. Yu. Figurina, “Optimal Control of the Rectilinear Motion of a Rigid Body on a Rough Plane by means of the Motion of Two Internal Masses,” J. Appl. Math. Mekh. 72, 126–135 (2008).
T. Yu. Figurina, “Optimal Motion Control for a System of Two Bodies on a Straight Line,” J. Comput. Syst. Sci. Int. 46, 227–23 (2007).
H. Li, K. Furuta, and F. L. Chernousko, “Motion Generation of the Capsubot Using Internal Force and Static Friction,” in Proc. Decision and Control, 45th IEEE Conference on Digital Object Identifier, 2006 (IEEE Conference Publications, 2006), pp. 6575–6580.
F. L. Chernousko, “Dynamics of a Body Controlled by Internal Motions,” in Proc. of IUTAM Symp. on Dynamics and Control of Nonlinear Systems with Uncertainty, Nanjing, China, 2006 (Springer, 2006), pp. 227–236.
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1963; Gordon and Breach, New York, 1986).
Author information
Authors and Affiliations
Additional information
Original Russian Text © A.A. Podosinnikova, 2012, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2012, No. 6, pp. 112–121.
Rights and permissions
About this article
Cite this article
Podosinnikova, A.A. Optimal control of dual-mass system motion in a medium with a piecewise linear resistance. J. Comput. Syst. Sci. Int. 51, 849–858 (2012). https://doi.org/10.1134/S106423071206010X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S106423071206010X