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2024 | OriginalPaper | Chapter

Dynamics of a Low-Inertia Ball Located Between Two Rotating Planes with Viscous Friction

Authors : Alexander Koshelev, Eugene Kugushev, Tatiana Shahova

Published in: Perspectives in Dynamical Systems I — Applications

Publisher: Springer International Publishing

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Abstract

The problem of the motion of a low-inertia ball between two horizontal uniformly rotating planes with linear viscous friction is considered. The center of mass of the ball coincides with its geometric center, the central inertia tensor of the ball is spherical. Two cases of low inertia of the ball are investigated: in the first case the mass of the ball is constant and concentrated near its center, in the second case the mass of the ball is small. In both cases the equations of motion of the ball have the form of the Tikhonov’s type equations with a small parameter in the left-hand side. The dynamics of the ball on an arbitrary finite time interval in the limit as the central moment of inertia of the ball tends to zero is studied.

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previous chapter Nonlinear Dynamics of a 2DOF Magneto-Mechanical Harvester
next chapter Determination of the Loading of an Open Car with Filler in the Center Sill
Literature
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Eldering, J.: Realizing nonholonomic dynamics as limit of friction forces. Regul. Chaotic Dyn., vol. 21, no. 4, pp. 390–409 (2016).MathSciNetCrossRef
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3.
Karapetyan, A.V., Rumyantsev, V.V.: Stability of conservative and dissipative systems. Itogi Nauki Tekh. Ser. Obshch. Mekh., vol. 6, VINITI, Moscow (1983)
4.
Milne, E.A.: Vectorial mechanics. Methuen Amp Co. Ltd., London (1948).
5.
Routh, E.J.: The advanced part of a treatise on the dynamics of a system of rigid bodies: being part II of a treatise on the whole subject. MacMillan , New York (1905).
6.
Tikhonov, A.N.: Systems of differential equations containing small parameters in the derivatives. Mat. Sb. (N.S.), 31(3), pp. 575–586 (1952).
Metadata
Title
Dynamics of a Low-Inertia Ball Located Between Two Rotating Planes with Viscous Friction
Authors
Alexander Koshelev
Eugene Kugushev
Tatiana Shahova
Copyright Year
2024
Book
Perspectives in Dynamical Systems I — Applications

Print ISBN: 978-3-031-56491-8

Electronic ISBN: 978-3-031-56492-5

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-56492-5_23

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