Аннотация:
We consider two problems from the rigid body dynamics and use new methods of stability and asymptotic behavior analysis for their solution. The first problem deals with motion of a rigid body in an unbounded volume of ideal fluid with zero vorticity. The second problem, having similar asymptotic behavior, is concerned with motion of a sleigh on an inclined plane. The equations of motion for the second problem are non-holonomic and exhibit some new features not typical for Hamiltonian systems. A comprehensive survey of references is given and new problems connected with falling motion of heavy bodies in fluid are proposed.
Образец цитирования:
A. V. Borisov, V. V. Kozlov, I. S. Mamaev, “Asymptotic stability and associated problems of dynamics of falling rigid body”, Regul. Chaotic Dyn., 12:5 (2007), 531–565
\RBibitem{BorKozMam07}
\by A. V. Borisov, V. V. Kozlov, I. S. Mamaev
\paper Asymptotic stability and associated problems of dynamics of falling rigid body
\jour Regul. Chaotic Dyn.
\yr 2007
\vol 12
\issue 5
\pages 531--565
\mathnet{http://mi.mathnet.ru/rcd637}
\crossref{https://doi.org/10.1134/S1560354707050061}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2350338}
\zmath{https://zbmath.org/?q=an:1229.37107}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd637
https://www.mathnet.ru/rus/rcd/v12/i5/p531
Эта публикация цитируется в следующих 39 статьяx:
Alexander A. Kilin, Anna M. Gavrilova, Elizaveta M. Artemova, “Dynamics of an Elliptic Foil with an Attached Vortex in an Ideal Fluid: The Integrable Case”, Regul. Chaot. Dyn., 2024
I. A. Bizyaev, E. V. Vetchanin, “Climb of the Chaplygin Sleigh on an Inclined Plane under Periodic Controls: Speedup and Uniform Motion”, Rus. J. Nonlin. Dyn., 20:4 (2024), 463–479
Ivan A. Bizyaev, Ivan S. Mamaev, “Qualitative Analysis of the Dynamics
of a Balanced Circular Foil and a Vortex”, Regul. Chaotic Dyn., 26:6 (2021), 658–674
Xu T., Li J., Li Zh., Liao Sh., “Accurate Predictions of Chaotic Motion of a Free Fall Disk”, Phys. Fluids, 33:3 (2021), 037111
E. V. Vetchanin, “The Motion of a Balanced Circular Cylinder in an Ideal Fluid Under the Action of External Periodic Force and Torque”, Rus. J. Nonlin. Dyn., 15:1 (2019), 41–57
Alexey V. Ivanov, “On Transversal Connecting Orbits of Lagrangian Systems in a Nonstationary Force Field: the Newton – Kantorovich Approach”, Regul. Chaotic Dyn., 24:4 (2019), 392–417
Borisov V A., Vetchanin E.V., Mamaev I.S., “Motion of a Smooth Foil in a Fluid Under the Action of External Periodic Forces. i”, Russ. J. Math. Phys., 26:4 (2019), 412–427
I. S. Mamaev, V. A. Tenenev, E. V. Vetchanin, “Dynamics of a Body with a Sharp Edge in a Viscous Fluid”, Nelin. Dinam., 14:4 (2018), 473–494
Alexey V. Borisov, Ivan S. Mamaev, Eugeny V. Vetchanin, “Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation”, Regul. Chaotic Dyn., 23:4 (2018), 480–502
Alexey V. Borisov, Ivan S. Mamaev, Evgeny V. Vetchanin, “Self-propulsion of a Smooth Body in a Viscous Fluid Under Periodic Oscillations of a Rotor and Circulation”, Regul. Chaotic Dyn., 23:7-8 (2018), 850–874
Ivan S. Mamaev, Evgeny V. Vetchanin, “The Self-propulsion of a Foil with a Sharp Edge in a Viscous Fluid Under the Action of a Periodically Oscillating Rotor”, Regul. Chaotic Dyn., 23:7-8 (2018), 875–886
А. А. Килин, А. И. Кленов, В. А. Тененев, “Управление движением тела с помощью внутренних масс в вязкой жидкости”, Компьютерные исследования и моделирование, 10:4 (2018), 445–460
С. В. Соколов, П. Е. Рябов, “Бифуркационная диаграмма системы двух вихрей в бозе-эйнштейновском конденсате, имеющих интенсивности одинаковых знаков”, Докл. РАН, 480:6 (2018), 652–656; S. V. Sokolov, P. E. Ryabov, “Bifurcation diagram of the two vortices in a Bose–Einstein condensate with intensities of the same signs”, Dokl. Math., 97:3 (2018), 286–290
Е. В. Ветчанин, А. И. Кленов, “Экспериментальные исследования падения винтовых тел в жидкости”, Нелинейная динам., 13:4 (2017), 585–598
А. В. Борисов, И. С. Мамаев, И. А. Бизяев, “Динамические системы с неинтегрируемыми связями: вакономная механика, субриманова геометрия и неголономная механика”, УМН, 72:5(437) (2017), 3–62; A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840
J.A. Somolinos, A. López, L.R. Núñez, R. Morales, “Dynamic model and experimental validation for the control of emersion manoeuvers of devices for marine currents harnessing”, Renewable Energy, 103 (2017), 333
Evgeny V. Vetchanin, Alexander A. Kilin, “Control of body motion in an ideal fluid using the internal mass and the rotor in the presence of circulation around the body”, J. Dyn. Control Syst., 23:2 (2017), 435–458
E. V. Vetchanin, I. S. Mamaev, “Optimal Control of the Motion of a Helical Body in a Liquid Using Rotors”, Russ. J. Math. Phys., 24:3 (2017), 399–411
Е. В. Ветчанин, А. А. Килин, “Управляемое движение твердого тела с внутренними механизмами в идеальной несжимаемой жидкости”, Современные проблемы механики, Сборник статей, Труды МИАН, 295, МАИК «Наука/Интерпериодика», М., 2016, 321–351; E. V. Vetchanin, A. A. Kilin, “Controlled motion of a rigid body with internal mechanisms in an ideal incompressible fluid”, Proc. Steklov Inst. Math., 295 (2016), 302–332
В. А. Тененев, Е. В. Ветчанин, Л. Ф. Илалетдинов, “Хаотическая динамика в задаче о падении тела винтовой формы в жидкости”, Нелинейная динам., 12:1 (2016), 99–120
Цитирование в формате AMSBIB
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