Abstract:
The motion of a heavy point on the surface of a rotating sphere is considered. It is assumed that the rotation axis does not coincide with the vertical diameter of the sphere and the angular velocity of the sphere is constant. The Lagrange equations for this system are derived. Sets of relative equilibria are found and their dependence on the parameters of the system is studied in extreme cases when the magnitude of the angular velocity or the distance between the rotation axis and the center of the sphere is large. The results are represented in graphic form. The same graphic series are also numerically plotted in the general case.
Keywords:
motion of a particle on a sphere, dry friction, relative equilibria.
Citation:
E. S. Shalimova, “On the motion of a material point on a rotating sphere with dry friction (the case of the vertical axis)”, Nelin. Dinam., 12:3 (2016), 369–383
\Bibitem{Sha16}
\by E.~S.~Shalimova
\paper On the motion of a material point on a rotating sphere with dry friction (the case of the vertical axis)
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 3
\pages 369--383
\mathnet{http://mi.mathnet.ru/nd533}
\crossref{https://doi.org/10.20537/nd1603006}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1834792}
\elib{https://elibrary.ru/item.asp?id=27328720}
Linking options:
https://www.mathnet.ru/eng/nd533
https://www.mathnet.ru/eng/nd/v12/i3/p369
This publication is cited in the following 8 articles:
A. A. Burov, V. I. Nikonov, E. S. Shalimova, “On the Motion of a Point Particle on a Homogeneous Gravitating Ball with a Spherical Inclusion”, Prikladnaâ matematika i mehanika, 88:2 (2024), 172
A. A. Burov, V. I. Nikonov, “On the Relative Equilibria of a Heavy Bead on a Uniformly Rotating Rough Spoke”, Mech. Solids, 58:3 (2023), 748
A. A. Burov, V. I. Nikonov, “Relative Equilibria of a Heavy Point on a Uniformly Rotating Inclined Plane”, Mech. Solids, 58:1 (2023), 131
A. A. Burov, V. I. Nikonov, “Relative Equilibria of a Heavy Point on a Uniformly Rotating Inclined Plane”, Izvestiya Rossiiskoi akademii nauk. Mekhanika tverdogo tela, 2023, no. 1, 156
A. A. Burov, V. I. Nikonov, “On the Relative Equilibria of a Heavy Bead on a Uniformly Rotating Rough Spoke”, Izvestiya Rossiiskoi akademii nauk. Mekhanika tverdogo tela, 2023, no. 3, 99
A. A. Burov, V. I. Nikonov, E. S. Shalimova, “On Relative Equilibria on the Surface of a Spherical Cavity Inside a Uniformly Rotating Gravitating Ball”, Mech. Solids, 57:8 (2022), 1862
A. A. Burov, V. I. Nikonov, E. S. Shalimova, “On the Motion of a Point Particle on a Homogeneous Gravitating Ball with a Spherical Cavity in the Presence of Dry Friction”, Mech. Solids, 56:8 (2021), 1587
Aleksandr Burov, Ivan Kosenko, Ekaterina Shalimova, “OB OTNOSITELNYKh RAVNOVESIYaKh MASSIVNOI TOChKI NA RAVNOMERNO VRASchAYuSchEMSYa ASTEROIDE”, Doklady Akademii nauk, 2017, no. 3, 269
Citation in format AMSBIB
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