Аннотация:
In 1913 A. D. Bilimovich observed that rheonomic constraints which are linear and homogeneous in generalized velocities are ideal. As a typical example, he considered rheonomic nonholonomic deformation of the Euler equations whose scleronomic version is equivalent to the nonholonomic Suslov system. For the Bilimovithch system, equations of motion are reduced to quadrature, which is discussed in rheonomic and scleronomic cases.
Ключевые слова:
rheonomic Lagrangian systems, nonholonomic mechanics, integrability by quadratures.
This work was supported by the Russian Science Foundation (project no. 19-71-30012) and performed at the Steklov Mathematical Institute of the Russian Academy of Sciences.
Поступила в редакцию: 20.01.2020 Исправленный вариант: 25.06.2020
Образец цитирования:
A. V. Borisov, A. V. Tsiganov, “On rheonomic nonholonomic deformations of the Euler equations proposed by Bilimovich”, Theor. Appl. Mech., 47:2 (2020), 155–168
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https://www.mathnet.ru/rus/tam83
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Эта публикация цитируется в следующих 5 статьяx:
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, 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 — Nonholonomic Systems
with Invariant Measures”, Regul. Chaotic Dyn., 27:4 (2022), 424–442
A. V. Borisov, A. V. Tsiganov, E. A. Mikishanina, “On inhomogeneous nonholonomic Bilimovich system”, Commun. Nonlinear Sci. Numer. Simul., 94 (2021), 105573–11
Alexey Borisov, Evgeniya Mikishanina, Andrey Tsiganov, 2020 International Conference Nonlinearity, Information and Robotics (NIR), 2020, 1
Цитирование в формате AMSBIB
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