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On the Moving Trajectory of a Ball in a Viscous Liquid between Two Concentric Rigid Spheres

Moscow Aviation Institute (National Research University), Moscow 125080, Russia
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Math. Comput. Appl. 2018, 23(4), 77; https://doi.org/10.3390/mca23040077
Received: 20 November 2018 / Accepted: 29 November 2018 / Published: 4 December 2018
(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
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Abstract

In the paper, the dynamic motion of a point ball with a mass of m , sliding in a viscous liquid between two concentric spheres under the influence of gravity and viscous and dry resistance, is investigated. In addition, it is considered that the ball starts its motion from some arbitrary point M 0 = M ( θ 0 , φ 0 ) . A system of nonlinear differential equations in a spheroidal coordinate system is obtained for the angular variables θ and φ to account for all the forces acting on the ball. The dependence of the reaction force on the angular variables is found, and the solution of the resulting system of equations is numerically analyzed. The projections of the trajectories on the plane x y ,   y z ,   x z are found. View Full-Text
Keywords: equations of curvilinear motion; classical mechanics; nonlinear dynamics equations of curvilinear motion; classical mechanics; nonlinear dynamics
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Gladkov, S.; Bogdanova, S. On the Moving Trajectory of a Ball in a Viscous Liquid between Two Concentric Rigid Spheres. Math. Comput. Appl. 2018, 23, 77.

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