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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
Understanding Reversals of a Rattleback
Stefan Rauch-Wojciechowskia, Maria Przybylskab a Department of Mathematics, Linköping University, 581 83 Linköping, Sweden
b Institute of Physics, University of Zielona Góra, Licealna 9, PL-65–417 Zielona Góra, Poland
Аннотация:
A counterintuitive unidirectional (say counterclockwise) motion of a toy rattleback takes place when it is started by tapping it at a long side or by spinning it slowly in the clockwise sense of rotation. We study the motion of a toy rattleback having an ellipsoidal-shaped bottom by using frictionless Newton equations of motion of a rigid body rolling without sliding in a plane. We simulate these equations for tapping and spinning initial conditions to see the contact trajectory, the force arm and the reaction force responsible for torque turning the rattleback in the counterclockwise sense of rotation. Long time behavior of such a rattleback is, however, quasi-periodic and a rattleback starting with small transversal oscillations turns in the clockwise direction.
Ключевые слова:
rattleback, rigid body dynamics, nonholonomic mechanics, numerical solutions
Финансовая поддержка |
Номер гранта |
National Science Centre (Narodowe Centrum Nauki)  |
DEC-2013/09/B/ST1/04130 |
M. P. has been supported by grant No. DEC-2013/09/B/ST1/04130 of the National Science Center of Poland. S. R. and M.P. gratefully acknowledge support of the Department of Mathematics of Linköping University for this work and for M. P. visit in Linköping. |
DOI:
https://doi.org/10.1134/S1560354717040037
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Тип публикации:
Статья
MSC: 37J60, 37J25, 70G45 Поступила в редакцию: 01.06.2017 Принята в печать:19.06.2017
Язык публикации: английский
Образец цитирования:
Stefan Rauch-Wojciechowski, Maria Przybylska, “Understanding Reversals of a Rattleback”, Regul. Chaotic Dyn., 22:4 (2017), 368–385
Цитирование в формате AMSBIB
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\paper Understanding Reversals of a Rattleback
\jour Regul. Chaotic Dyn.
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\issue 4
\pages 368--385
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Образцы ссылок на эту страницу:
http://mi.mathnet.ru/rcd261 http://mi.mathnet.ru/rus/rcd/v22/i4/p368
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
Эта публикация цитируется в следующих статьяx:
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А. В. Борисов, И. С. Мамаев, И. А. Бизяев, “Динамические системы с неинтегрируемыми связями: вакономная механика, субриманова геометрия и неголономная механика”, УМН, 72:5(437) (2017), 3–62
; A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840 -
A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Comment on “Confining rigid balls by mimicking quadrupole ion trapping” [Am. J. Phys. 85, 821 (2017)]”, Am. J. Phys., 87:11 (2019), 935–938
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S. Jones, H. E. M. Hunt, “Rattlebacks for the rest of us”, Am. J. Phys., 87:9 (2019), 699–713
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B. Gajic, B. Jovanovic, “Nonholonomic connections, time reparametrizations, and integrability of the rolling ball over a sphere”, Nonlinearity, 32:5 (2019), 1675–1694
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