Next Article in Journal
Nanofluid Convective Heat Transfer Enhancement Elliptical Tube inside Circular Tube under Turbulent Flow
Next Article in Special Issue
On a Problem Arising in Application of the Re-Quantization Method to Construct Asymptotics of Solutions to Linear Differential Equations with Holomorphic Coefficients at Infinity
Previous Article in Journal
Some Notes to Extend the Study on Random Non-Autonomous Second Order Linear Differential Equations Appearing in Mathematical Modeling
Article Menu
Issue 4 (December) cover image

Export Article

Open AccessArticle

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
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2018, 23(4), 77;
Received: 20 November 2018 / Accepted: 29 November 2018 / Published: 4 December 2018
(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
PDF [934 KB, uploaded 4 December 2018]
  |     |  


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

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

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.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics



[Return to top]
Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top