Аннотация:
The paper considers two new integrable systems which go back to Chaplygin. The systems consist of a spherical shell that rolls on a plane; within the shell there is a ball or Lagrange’s gyroscope. All necessary first integrals and an invariant measure are found. The solutions are shown to be expressed in terms of quadratures.
This research was supported by the Grant of the Government of the Russian Federation
for state support of scientific research conducted under supervision of leading scientists in
Russian educational institutions of higher professional education (contract no. 11.G34.31.0039)
and the Federal target programme “Scientific and Scientific-Pedagogical Personnel of Innovative
Russia”, measure 1.1. “Scientific-Educational Center Regular and Chaotic Dynamics” (project
code 02.740.11.0195), measure 1.5 “Topology and Mechanics” (project code 14.740.11.0876).
Поступила в редакцию: 14.08.2011 Принята в печать: 29.11.2011
Образец цитирования:
Alexey V. Borisov, Ivan S. Mamaev, “Two Non-holonomic Integrable Problems Tracing Back to Chaplygin”, Regul. Chaotic Dyn., 17:2 (2012), 191–198
\RBibitem{BorMam12}
\by Alexey V.~Borisov, Ivan S.~Mamaev
\paper Two Non-holonomic Integrable Problems Tracing Back to Chaplygin
\jour Regul. Chaotic Dyn.
\yr 2012
\vol 17
\issue 2
\pages 191--198
\mathnet{http://mi.mathnet.ru/rcd339}
\crossref{https://doi.org/10.1134/S1560354712020074}
\zmath{https://zbmath.org/?q=an:1252.76056}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd339
https://www.mathnet.ru/rus/rcd/v17/i2/p191
Эта публикация цитируется в следующих 23 статьяx:
E. A. Mikishanina, “Two Ways to Control a Pendulum-Type Spherical Robot on a Moving Platform in a Pursuit Problem”, Mech. Solids, 59:1 (2024), 127
E. A. Mikishanina, “Algorithm for Controlling a Spherical Robot with a Pendulum Actuator in the Problem of Pursuing and Hitting a Moving Target”, Russ. Engin. Res., 44:5 (2024), 647
E. A. Mikishanina, “Two Ways to Control a Pendulum-Type Spherical Robot on a Moving Platform in a Pursuit Problem”, Izvestiâ Rossijskoj akademii nauk. Mehanika tverdogo tela, 2024, № 1, 230
A. A. Kilin, T. B. Ivanova, “The Integrable Problem of the Rolling Motion
of a Dynamically Symmetric Spherical Top
with One Nonholonomic Constraint”, Rus. J. Nonlin. Dyn., 19:1 (2023), 3–17
Alexander A. Kilin, Tatiana B. Ivanova, Elena N. Pivovarova, “Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base Using Feedback”, Regul. Chaotic Dyn., 28:6 (2023), 888–905
Alexey V. Borisov, Alexander P. Ivanov, “A Top on a Vibrating Base:
New Integrable Problem of Nonholonomic Mechanics”, Regul. Chaotic Dyn., 27:1 (2022), 2–10
Ivanova T.B. Karavaev Yu.L. Kilin A.A., “Control of a Pendulum-Actuated Spherical Robot on a Horizontal Plane With Rolling Resistance”, Arch. Appl. Mech., 92:1 (2022), 137–150
E. A. Mikishanina, “Motion Control of a Spherical Robot with a Pendulum
Actuator for Pursuing a Target”, Rus. J. Nonlin. Dyn., 18:5 (2022), 899–913
Alexander A. Kilin, Elena N. Pivovarova, “Stability and Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base”, Regul. Chaotic Dyn., 25:6 (2020), 729–752
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Different Models of Rolling for a Robot Ball on a Plane as a Generalization of the Chaplygin Ball Problem”, Regul. Chaotic Dyn., 24:5 (2019), 560–582
Ivanova T.B. Kilin A.A. Pivovarova E.N., “Controlled Motion of a Spherical Robot With Feedback. II”, J. Dyn. Control Syst., 25:1 (2019), 1–16
Ivanova T.B. Kilin A.A. Pivovarova E.N., “Controlled Motion of a Spherical Robot With Feedback. i”, J. Dyn. Control Syst., 24:3 (2018), 497–510
Т. Б. Иванова, А. А. Килин, Е. Н. Пивоварова, “Управление качанием сфероробота на наклонной плоскости”, Докл. РАН, 482:6 (2018), 655–660; A. A. Kilin, T. B. Ivanova, E. N. Pivovarova, “Control of the rolling motion of a spherical robot on an inclined plane”, Dokl. Phys., 63:10 (2018), 435–440
А. А. Килин, Е. Н. Пивоварова, Т. Б. Иванова, “Управляемое движение сферического робота маятникового типа на наклонной плоскости”, Докл. РАН, 481:3 (2018), 258–263; A. A. Kilin, T. B. Ivanova, E. N. Pivovarova, “Controlled motion of a spherical robot of pendulum type on an inclined plane”, Dokl. Phys., 63:7 (2018), 302–306
Alexander A. Kilin, Elena N. Pivovarova, Tatyana B. Ivanova, “Spherical Robot of Combined Type: Dynamics and Control”, Regul. Chaotic Dyn., 20:6 (2015), 716–728
Pantelis A. Damianou, Hervé Sabourin, Pol Vanhaecke, “Intermediate Toda Systems”, Regul. Chaotic Dyn., 20:3 (2015), 277–292
А. А. Килин, Ю. Л. Караваев, “Экспериментальные исследования динамики сферического робота комбинированного типа”, Нелинейная динам., 11:4 (2015), 721–734
A. A. Kilin, Y. L. Karavaev, “Experimental research of dynamic of spherical robot of combined type”, Nelin. Dinam., 2015, 721
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Dynamics of Nonholonomic Systems Consisting of a
Spherical Shell with a Moving Rigid Body Inside”, Regul. Chaotic Dyn., 19:2 (2014), 198–213
Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “The Hierarchy of Dynamics of a Rigid Body Rolling without Slipping and Spinning on a Plane and a Sphere”, Regul. Chaotic Dyn., 18:3 (2013), 277–328
Цитирование в формате AMSBIB
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