Аннотация:
We consider the multi-dimensional generalisation of the problem of a sphere, with axi-symmetric mass distribution, that rolls without slipping or spinning over a plane. Using recent results from García-Naranjo [21] and García-Naranjo and Marrero [22], we show that the reduced equations of motion possess an invariant measure and may be represented in Hamiltonian form by Chaplygin's reducing multiplier method.
We also prove a general result on the existence of first integrals for certain Hamiltonisable Chaplygin systems with internal symmetries that is used to determine conserved quantities of the problem.
Ключевые слова:
nonholonomic systems, Hamiltonisation, multi-dimensional rigid body dynamics, symmetries and reduction, Chaplygin systems.
The author acknowledges the Alexander von Humboldt Foundation for a Georg Forster Experienced Researcher Fellowship that funded a research visit to TU Berlin where this work was done.
Поступила в редакцию: 30.01.2019 Исправленный вариант: 07.04.2019
Образец цитирования:
Luis C. García-Naranjo, “Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere”, Theor. Appl. Mech., 46:1 (2019), 65–88
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\paper Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere
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https://www.mathnet.ru/rus/tam55
https://www.mathnet.ru/rus/tam/v46/i1/p65
Эта публикация цитируется в следующих 6 статьяx:
Luis C. García-Naranjo, Juan C. Marrero, David Martín de Diego, Paolo E. Petit Valdés, “Almost-Poisson Brackets for Nonholonomic Systems with Gyroscopic Terms and Hamiltonisation”, J Nonlinear Sci, 34:6 (2024)
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
Salvatore Federico, Mawafag F. Alhasadi, “Inverse dynamics in rigid body mechanics”, Theor. Appl. Mech., 49:2 (2022), 157–181
Luis C García-Naranjo, Juan C Marrero, “The geometry of nonholonomic Chaplygin systems revisited”, Nonlinearity, 33:3 (2020), 1297
Цитирование в формате AMSBIB
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