Open AccessTranslational Rectilinear Motion of a Solid Body Carrying a Movable Inner Mass
Author(s) -
B. S. Bardin,
B. S. Bardin,
A. S. Panev,
A. S. Panev
Publication year - 2019
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2019-65-4-557-592
Subject(s) - center of mass (relativistic) , motion (physics) , dynamics (music) , solid body , classical mechanics , physics , mechanics , plane (geometry) , rest (music) , point (geometry) , circular motion , added mass , surface (topology) , periodic function , constant (computer programming) , inclined plane , geometry , mathematics , quantum mechanics , energy–momentum relation , acoustics , vibration , computer science , programming language
We consider the motion of the mechanical system consisting of the case (a solid body) and the inner mass (a material point). The inner mass circulates inside the case on a circle centered at the center of mass of the case. We suppose that absolute value of the velocity of circular motion of the inner mass is constant. The case moves translationally and rectilinearly on a flat horizontal surface with forces of viscous friction and dry Coulomb friction on it. The inner mass moves in vertical plane. We perform the full qualitative investigation of the dynamics of this system. We prove that there always exist a unique motion of the case with periodic velocity. We study all possible types of such a periodic motion. We establish that for any initial velocity, the case either reaches the periodic mode of motion in a finite time or asymptotically approaches to it depending on the parameters of the problem.