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

Mathematical and Computational Applications

Bogdanova, Sophie¹  Gladkov, Sergey² 

[1] Author to whom correspondence should be addressed.;Moscow Aviation Institute (National Research University), Moscow 125080, Russia

关键词: equations of curvilinear motion;    classical mechanics;    nonlinear dynamics;   

DOI  :  10.3390/mca23040077

学科分类：计算数学

来源: mdpi

【 摘 要 】

In the paper, the dynamic motion of a point ball with a mass ofm , 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 pointM 0= M( θ 0,φ 0 ) . A system of nonlinear differential equations in a spheroidal coordinate system is obtained for the angular variablesθandφto 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.

【 授权许可】

CC BY