Abstract:
The problem of motion of a heavy particle on a sphere uniformly rotating about a fixed axis is considered in the case of dry friction. It is assumed that the angle of inclination of the rotation axis is constant. The existence of equilibria in an absolute coordinate system and their linear stability are discussed. The equilibria in a relative coordinate system rotating with the sphere are also studied. These equilibria are generally nonisolated. The dependence of the equilibrium sets of this kind on the system parameters is also considered.
Keywords:
dry friction, motion of a particle on a sphere, absolute and relative equilibria, bifurcations of equilibria.
Citation:
Alexander A. Burov, Ekaterina S. Shalimova, “On the Motion of a Heavy Material Point on a Rotating Sphere (Dry Friction Case)”, Regul. Chaotic Dyn., 20:3 (2015), 225–233
\Bibitem{BurSha15}
\by Alexander A. Burov, Ekaterina S. Shalimova
\paper On the Motion of a Heavy Material Point on a Rotating Sphere (Dry Friction Case)
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 3
\pages 225--233
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Linking options:
https://www.mathnet.ru/eng/rcd30
https://www.mathnet.ru/eng/rcd/v20/i3/p225
This publication is cited in the following 9 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, “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, 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
A. A. Burov, A. D. Guerman, V. I. Nikonov, “Force field properties and regions of particle accumulation on asteroid surface”, Acta Astronaut., 174 (2020), 236–240
A. A. Burov, I. I. Kosenko, E. S. Shalimova, “Relative equilibria of a massive point on a uniformly rotating asteroid”, Dokl. Phys., 62:7 (2017), 359–362
Aleksandr Burov, Ivan Kosenko, Ekaterina Shalimova, “OB OTNOSITELNYKh RAVNOVESIYaKh MASSIVNOI TOChKI NA RAVNOMERNO VRASchAYuSchEMSYa ASTEROIDE”, Doklady Akademii nauk, 2017, no. 3, 269
E. S. Shalimova, “O dvizhenii tyazheloi tochki po sfere, vraschayuscheisya vokrug ne prokhodyaschei cherez ee tsentr vertikalnoi osi, pri nalichii sukhogo treniya”, Nelineinaya dinam., 12:3 (2016), 369–383
Citation in format AMSBIB
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