Аннотация:
In this paper we consider the dynamics of a rigid body with a sharp edge in contact with a rough plane. The body can move so that its contact point is fixed or slips or loses contact with the support. In this paper, the dynamics of the system is considered within three mechanical models which describe different regimes of motion. The boundaries of the domain of definition of each model are given, the possibility of transitions from one regime to another and their consistency with different coefficients of friction on the horizontal and inclined surfaces are discussed.
Ключевые слова:
rod, Painlevé paradox, dry friction, loss of contact, frictional impact.
This research was supported by the analytical departmental target program “Development of
Scientific Potential of Higher Schools” for 2012–2014, No 1.1248.2011 “Nonholonomic Dynamical
Systems and Control Problems” and by the Grant of the President of the Russian Federation for
Support of Leading Scientific Schools NSh-2964.2014.1. The work of T. B.Ivanova was supported by
the Grant of the President of the Russian Federation for Support of Young Candidates of Science
MK-2171.2014.1.
Поступила в редакцию: 28.03.2013 Принята в печать: 31.12.2013
Образец цитирования:
Ivan S. Mamaev, Tatiana B. Ivanova, “The Dynamics of a Rigid Body with a Sharp Edge in Contact with an Inclined Surface in the Presence of Dry Friction”, Regul. Chaotic Dyn., 19:1 (2014), 116–139
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\paper The Dynamics of a Rigid Body with a Sharp Edge in Contact with an Inclined Surface in the Presence of Dry Friction
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd144
https://www.mathnet.ru/rus/rcd/v19/i1/p116
Эта публикация цитируется в следующих 17 статьяx:
Alexander A. Kilin, Elena N. Pivovarova, “Dynamics of an Unbalanced Disk
with a Single Nonholonomic Constraint”, Regul. Chaotic Dyn., 28:1 (2023), 78–106
Г. М. Розенблат, “О РАВНОВЕСИИ ТВЕРДОГО ТЕЛА, ОПИРАЮЩЕГОСЯ ОДНОЙ ТОЧКОЙ НА ШЕРОХОВАТУЮ ПЛОСКОСТЬ”, Известия Российской академии наук. Механика твердого тела, 2023, № 6, 3
G. M. Rosenblat, “On the Equilibrium of a Solid Supported by a Single Point on a Rigid Plane”, Mech. Solids, 58:6 (2023), 1929
Alexander A. Kilin, Elena N. Pivovarova, “Motion control of the spherical robot rolling on a vibrating plane”, Applied Mathematical Modelling, 109 (2022), 492
Rozenblat G.M., “Equilibrium of a Solid Body Supported At One Point By a Rough Plane”, Dokl. Phys., 66:10 (2021), 296–302
Alexander N. Evgrafov, Gennady N. Petrov, Sergey A. Evgrafov, Lecture Notes in Mechanical Engineering, Advances in Mechanical Engineering, 2020, 75
А. В. Борисов, А. А. Килин, Ю. Л. Караваев, “О попятном движении катящегося диска”, УФН, 187:9 (2017), 1003–1006; A. V. Borisov, A. A. Kilin, Yu. L. Karavaev, “Retrograde motion of a rolling disk”, Phys. Usp., 60:9 (2017), 931–934
T. B. Ivanova, N. N. Erdakova, Yu. L. Karavaev, “Experimental investigation of the dynamics of a brake shoe”, Dokl. Phys., 61:12 (2016), 611–614
A. R. Champneys, P. L. Varkonyi, “The Painlevé paradox in contact mechanics”, IMA J. Appl. Math., 81:3, SI (2016), 538–588
B. Brogliato: Brogliato, B, Nonsmooth Mechanics: Models, Dynamics and Control, Communications and Control Engineering, 3Rd Edition, Springler, 2016
T. B. Ivanova, I. S. Mamaev, “Dynamics of a Painlevé–Appell system”, J. Appl. Math. Mech., 80:1 (2016), 7–15
Ю. Л. Караваев, А. А. Килин, “Динамика сфероробота с внутренней омниколесной платформой”, Нелинейная динам., 11:1 (2015), 187–204
А. В. Борисов, И. С. Мамаев, “Замечания о новых моделях трения и неголономной механике”, УФН, 185:12 (2015), 1339–1341; A. V. Borisov, I. S. Mamaev, “Notes on new friction models and nonholonomic mechanics”, Phys. Usp., 58:12 (2015), 1220–1222
Zh. Zhao, C. Liu, B. Chen, B. Brogliato, “Asymptotic analysis of Painlevé's paradox”, Multibody Syst. Dyn., 35:3 (2015), 299–319
Yury L. Karavaev, Alexander A. Kilin, “The Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform”, Regul. Chaotic Dyn., 20:2 (2015), 134–152
Alexander P. Ivanov, “On the Impulsive Dynamics of M-blocks”, Regul. Chaotic Dyn., 19:2 (2014), 214–225
Yizhar Or, “Painlevé’s Paradox and Dynamic Jamming in Simple Models of Passive Dynamic Walking”, Regul. Chaotic Dyn., 19:1 (2014), 64–80
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