Abstract:
We consider a vibration-driven system which consists of a rigid body and an internal mass. The internal mass is a particle moving in a circle inside the body. The center of the circle is located at the mass center of the body and the absolute value of particle velocity is a constant. The body performs rectilinear motion on a horizontal plane, whereas the particle moves in a vertical plane. We suppose that dry friction acts between the plane and the body.
We have investigated the dynamics of the above system in detail and given a full description of the body’s motion for any values of its initial velocity. In particular, it is shown that there always exists a periodic mode of motion. Depending on parameter values, one of three types of this periodic mode takes place. At any initial velocity the body either enters a periodic mode during a finite time interval or it asymptotically approaches the periodic mode.
Citation:
Bardin B. S., Panev A. S., “On the Motion of a Body with a Moving Internal Mass on a Rough Horizontal Plane”, Nelin. Dinam., 14:4 (2018), 519–542
\Bibitem{BarPan18}
\by Bardin B. S., Panev A. S.
\paper On the Motion of a Body with a Moving Internal Mass on a Rough Horizontal Plane
\jour Nelin. Dinam.
\yr 2018
\vol 14
\issue 4
\pages 519--542
\mathnet{http://mi.mathnet.ru/nd629}
\crossref{https://doi.org/10.20537/nd180407}
\elib{https://elibrary.ru/item.asp?id=36686072}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85061720180}
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https://www.mathnet.ru/eng/nd629
https://www.mathnet.ru/eng/nd/v14/i4/p519
This publication is cited in the following 4 articles:
Tatiana Figurina, Dmitri Knyazkov, “Motion of a system of interacting bodies in a medium with quadratic resistance”, Nonlinear Dyn, 112:1 (2024), 273
Tatiana Figurina, Dmitri Knyazkov, “Periodic regimes of motion of capsule system on rough plane”, Meccanica, 58:2-3 (2023), 493
Tatiana Figurina, Dmitri Knyazkov, “Periodic gaits of a locomotion system of interacting bodies”, Meccanica, 57:7 (2022), 1463
Dosaev M., Samsonov V., Hwang Sh.-Sh., “Construction of Control Algorithm in the Problem of the Planar Motion of a Friction-Powered Robot With a Flywheel and An Eccentric Weight”, Appl. Math. Model., 89:2 (2021), 1517–1527
Citation in format AMSBIB
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