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Dynamics of Two Interconnected Mass Points in a Resistive Medium

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Abstract

The problem of motion of two interconnected mass points in a resistive medium under periodic change of distance between them is considered. It is shown that a necessary condition for the locomotion (displacement of the center of mass) is the nonlinear law of resistance (dry or nonlinear viscous friction). If the mass points are identical, any periodic control law leads to a displacement of the center of mass only in the presence of anisotropic (asymmetrical) friction. If there are different masses, motion is possible also with isotropic friction law under the action of a periodic control law. In the paper such special laws for the control of the velocity and the direction of motion are presented. The friction is assumed to be small and the investigations are based on the method of averaging. By means of this method analytical dependence of the velocity of motion is obtained.

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Authors and Affiliations

  1. Faculty for Mechanical Engineering, Technische Universitaet Ilmenau, PF 10 05 65, 98684, Ilmenau, Germany

    Klaus Zimmermann, Igor Zeidis & Mikhail Pivovarov

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  1. Klaus Zimmermann
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  2. Igor Zeidis
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  3. Mikhail Pivovarov
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Correspondence to Igor Zeidis.

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Zimmermann, K., Zeidis, I. & Pivovarov, M. Dynamics of Two Interconnected Mass Points in a Resistive Medium. Differ Equ Dyn Syst 21, 21–28 (2013). https://doi.org/10.1007/s12591-012-0116-8

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  • DOI: https://doi.org/10.1007/s12591-012-0116-8

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