Аннотация:
We present an integrable nonholonomic case of rolling without sliding of a gyroscopic ball over a sphere. This case was introduced and studied in detail by Vasilije Demchenko in his 1923 doctoral dissertation defended at the University of Belgrade, with Anton Bilimović as the advisor. These results are absolutely unknown to modern researchers. The study is based on the C. Neumann coordinates and the Voronec principle. By using the involved technique of elliptic functions, a detailed study of motion is performed. Several special classes of trajectories are distinguished, including regular and pseudo-regular precessions. The so-called remarkable trajectories, introduced by Paul Painlevé and Anton Bilimović, are described in the present case. The historical context of the results as well as their place in contemporary mechanics are outlined.
Ключевые слова:
nonholonimic dynamics, rolling without sliding, C. Neumann coordinates, elliptic functions, elliptic integrals, Voronec principle, regular and pseudo-regular precessions, remarkable trajectories.
This research has been partially supported by the Mathematical Institute of the Serbian Academy of Sciences and Arts and the Ministry of Education, Science, and Technological Development of Serbia.
Поступила в редакцию: 06.11.2020 Исправленный вариант: 30.11.2020
Образец цитирования:
Vladimir Dragović, Borislav Gajić, Božidar Jovanović, “Demchenko's nonholonomic case of a gyroscopic ball rolling without sliding over a sphere after his 1923 Belgrade doctoral thesis”, Theor. Appl. Mech., 47:2 (2020), 257–287
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\paper Demchenko's nonholonomic case of a gyroscopic ball rolling without sliding over a sphere after his 1923 Belgrade doctoral thesis
\jour Theor. Appl. Mech.
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/tam89
https://www.mathnet.ru/rus/tam/v47/i2/p257
Эта публикация цитируется в следующих 3 статьяx:
Vladimir Dragović, Borislav Gajić, Božidar Jovanović, “Gyroscopic Chaplygin Systems and Integrable Magnetic Flows on Spheres”, J Nonlinear Sci, 33:3 (2023)
Vladimir Dragović, Borislav Gajić, Bozidar Jovanović, “Spherical and Planar Ball Bearings — a Study of Integrable Cases”, Regul. Chaotic Dyn., 28:1 (2023), 62–77
Vladimir Dragović, Borislav Gajić, Bozidar Jovanović, “Spherical and Planar Ball Bearings — Nonholonomic Systems
with Invariant Measures”, Regul. Chaotic Dyn., 27:4 (2022), 424–442
Цитирование в формате AMSBIB
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