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This article is cited in 5 scientific papers (total in 5 papers)
Hamiltonisation, measure preservation and first integrals of the multi-dimensional rubber Routh sphere
Luis C. García-Naranjo Departamento de Matemáticas y Mecánica, IIMAS-UNAM, Mexico City, Mexico
Abstract:
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.
Keywords:
nonholonomic systems, Hamiltonisation, multi-dimensional rigid body dynamics, symmetries and reduction, Chaplygin systems.
Received: 30.01.2019 Revised: 07.04.2019
Citation:
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
Linking options:
https://www.mathnet.ru/eng/tam55 https://www.mathnet.ru/eng/tam/v46/i1/p65
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Abstract page: | 145 | Full-text PDF : | 41 | References: | 21 |
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