Analytical solution of problem on fall of sphere the radius of which decreases from linear-fractional law
Journal Title: Технічна механіка, Техническая механика, Technical Mechanics - Year 2014, Vol 2, Issue 2
Abstract
The paper deals with building a mathematical model of motion of the sphere with variable radius and mass. The analytical method for solving the Cauchy problem for a nonlinear equation of motion with variable coeffi-cients is the research method. For the first time a closed analytic solution of a nonlinear differential equation of a vertical fall of a spherical variable-mass body is built in cylindrical functions when its radius is reduced fraction-ally and linearly in time and quadratic resistance of the air environment. The asymptotic behavior of solutions is investigated.
Authors and Affiliations
V. Olshansky, S. Olshansky
Keywords
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