Аннотация:
In this paper we investigate the dynamics of a body with a flat base sliding on a horizontal and inclined rough plane under the assumption of linear pressure distribution of the body on the plane as the simplest dynamically consistent friction model. For analysis we use the descriptive function method similar to the methods used in the problems of Hamiltonian dynamics with one degree of freedom and allowing a qualitative analysis of the system to be made without explicit integration of equations of motion. In addition, we give a systematic review of the well-known experimental and theoretical results in this area.
This work was supported by the Ministry of Education and Science of the Russian Federation
within the framework of the basic part of the state assignment to institutions of higher education.
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 and by the RFBR Grant 14-01-00289-a.
Поступила в редакцию: 02.09.2014 Принята в печать: 16.10.2014
Образец цитирования:
Alexey V. Borisov, Nadezhda N. Erdakova, Tatiana B. Ivanova, Ivan S. Mamaev, “The Dynamics of a Body with an Axisymmetric Base Sliding on a Rough Plane”, Regul. Chaotic Dyn., 19:6 (2014), 607–634
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\by Alexey~V.~Borisov, Nadezhda~N.~Erdakova, Tatiana~B.~Ivanova, Ivan~S.~Mamaev
\paper The Dynamics of a Body with an Axisymmetric Base Sliding on a Rough Plane
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 6
\pages 607--634
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\crossref{https://doi.org/10.1134/S1560354714060021}
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd187
https://www.mathnet.ru/rus/rcd/v19/i6/p607
Эта публикация цитируется в следующих 16 статьяx:
Kpomahou Yelome Judicael Fernando Hinvi L.A. Adechinan J.A. Miwadinou C.H., “Chaotic Dynamics of a Mixed Rayleigh-Lienard Oscillator Driven By Parametric Periodic Damping and External Excitations”, Complexity, 2021 (2021), 6631094
Ivanova T.B., “Non-holonomic rolling of a ball on the surface of a rotating cylinder”, ZAMM-Z. Angew. Math. Mech., 100:12 (2020), e202000067
Kireenkov A.A. Zhavoronok I S., “Anisotropic Combined Dry Friction in Problems of Pneumatics' Dynamics”, J. Vib. Eng. Technol., 8:2, SI (2020), 365–372
И. Г. Горячева, А. А. Зобова, “Динамика упругого цилиндра на упругом основании”, ПММ, 83:1 (2019), 39–46; I. G. Goryacheva, A. A. Zobova, “Dynamics of the motion of an elastic cylinder along an elastic foundation”, Mech. Sol., 54:2 (2019), 271–277
V A. Borisov, T. B. Ivanova, Yu. L. Karavaev, I. S. Mamaev, “Theoretical and Experimental Investigations of the Rolling of a Ball on a Rotating Plane (turntable)”, Eur. J. Phys., 39:6 (2018), 065001
N. A. Kudryashov, D. I. Sinelshchikov, “On the Integrability Conditions for a Family of Liénard-type Equations”, Regul. Chaotic Dyn., 21:5 (2016), 548–555
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. P. Ivanov, N. N. Erdakova, “On a mechanical lens”, Int. J. Non-Linear Mech., 79 (2016), 115–121
Alexey V. Borisov, Ivan S. Mamaev, Nadezhda N. Erdakova, “Dynamics of a body sliding on a rough plane and supported at three points”, Theor. Appl. Mech., 43:2 (2016), 169–190
Ю. Л. Караваев, А. А. Килин, “Динамика сфероробота с внутренней омниколесной платформой”, Нелинейная динам., 11:1 (2015), 187–204
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov, “On the Connection of the Quadratic Lienard Equation with an Equation for the Elliptic Functions”, Regul. Chaotic Dyn., 20:4 (2015), 486–496
Nikolay A. Kudryashov, “Analytical Solutions of the Lorenz System”, Regul. Chaotic Dyn., 20:2 (2015), 123–133
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
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
А. В. Борисов, Ю. Л. Караваев, И. С. Мамаев, Н. Н. Ердакова, Т. Б. Иванова, В. В. Тарасов, “Экспериментальное исследование движения тела с осесимметричным основанием, скользящего по шероховатой плоскости”, Нелинейная динам., 11:3 (2015), 547–577
Alexey V. Borisov, Yury L. Karavaev, Ivan S. Mamaev, Nadezhda N. Erdakova, Tatyana B. Ivanova, Valery V. Tarasov, “Experimental Investigation of the Motion of a Body with an Axisymmetric Base Sliding on a Rough Plane”, Regul. Chaotic Dyn., 20:5 (2015), 518–541
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