 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 44, Issue 5 / 2009 | Next article >> |
| V.P. Ol'shanskii and S.V. Ol'shanskii, "On the Vertical Ascent of a Spherical Body of Increasing Mass," Mech. Solids. 44 (5), 671-676 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
5 |
Pages |
671-676 |
| DOI |
10.3103/S0025654409050033 |
| Title |
On the Vertical Ascent of a Spherical Body of Increasing Mass |
| Author(s) |
V.P. Ol'shanskii (Petro Vasilenko Kharkov National Technical University of Agriculture, Artema 44, Kharkov, 61002 Ukraine)
S.V. Ol'shanskii (Petro Vasilenko Kharkov National Technical University of Agriculture, Artema 44, Kharkov, 61002 Ukraine, stasolsh@mail.ru) |
| Abstract |
We show that if the dependence of the drag force on the velocity is quadratic and the time dependence of the radius of a spherical body is linear, then the first integral of the equation of motion can be written out in closed form in terms of Bessel functions. To calculate the second integral, we propose concise approximate formulas. Their accuracy is verified by comparing the results obtained by analytic and numerical solution of the Cauchy problem. |
| Keywords |
spherical particle, increasing radius, mass variability, vertical motion, special functions |
| References |
| 1. | I. V. Meshcherskii, Works on the Mechanics of Bodies of
Variable Mass (Gostekhizdat, Moscow, 1952) [in Russian]. |
| 2. | I. V. Meshcherskii,
Collection of Problems in Theoretical Mechanics
(Nauka, Moscow, 1986)
[in Russian]. |
| 3. | V. P. Ol'shanskii and S. V. Ol'shanskii,
"On Nonlinear Model of Fall of a Vaporizing Droplet
as a Material Point of Variable Mass,"
Mekh. Mashinostr.,
No. 1, 23-28 (2006). |
| 4. | M. Abramowitz and I. A. Stegun (Editors),
Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables
(Dover, New York, 1972; Nauka, Moscow, 1979). |
| 5. | I. F. Obraztsov, B. V. Nerubailo, and I. V. Andrianov,
Asymptotic Methods in the Structural Mechanics of Thin-Walled Structures
(Mashinostroenie, Moscow, 1991)
[in Russian]. |
| 6. | N. N. Kalitkin,
Numerical Methods
(Nauka, Moscow, 1978)
[in Russian]. |
|
| Received |
11 April 2007 |
| Link to Fulltext |
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