Edit Profile (opens in new tab) Borisov, Alekseĭ Vladimirovich Compute Distance To: Compute Author ID: borisov.alexey-v Published as: Borisov, A. V.; Borisov, Alexey V.; Borisov, Alexey; Borisov, Alekseĭ Vladimirovich; Borisev, Alexey V.; Borisov, Alexei V. more...less Further Spellings: Борисов Алексей Владимирович Homepage: http://ics.org.ru/staff/detail/23-alexey_borisov?menu=mi_person&persid=2 External Links: ORCID · Wikidata · Math-Net.Ru Documents Indexed: 181 Publications since 1996, including 6 Books 5 Contributions as Editor · 1 Further Contribution Biographic References: 3 Publications Co-Authors: 58 Co-Authors with 182 Joint Publications 1,283 Co-Co-Authors all top 5 Co-Authors 4 single-authored 140 Mamaev, Ivan Sergeevich 39 Kilin, Aleksandr Aleksandrovich 30 Bizyaev, Ivan Alekseevich 8 Bolsinov, Alexey V. 8 Tsyganov, Andreĭ Vladimirovich 7 Kozlov, Valeriĭ Vasil’evich 6 Ramodanov, Sergey M. 5 Ivanova, Tatiana B. 5 Kazakov, Alexey O. 5 Mikishanina, Evgeniya Arifzhanovna 4 Erdakova, Nadezhda N. 4 Sataev, Igor’ Rustamovich 3 Karavaev, Yurĭ Leonidovich 3 Kuznetsov, Sergey P. 3 Sokolov, Sergeĭ Viktorovich 3 Treshchev, Dmitriĭ Valer’evich 2 Bolotin, Sergeĭ Vladimirovich 2 Dragović, Vladimir 2 Ivanov, Aleksandr Pavlovich 2 Lebedev, V. G. 2 Ryabov, Pavel Evgen’evich 2 Sokolovskiy, Mikhail A. 2 Tsygvintsev, Alexei V. 2 Vetchanin, Evgeniĭ Vladimirovich 1 Derr, Vasiliĭ Yakovlevich 1 Dudoladov, S. L. 1 Fedorov, Yuri N. 1 García-Naranjo, Luis C. 1 Gonchenko, Sergey V. 1 Gryzlov, Anatoliĭ Aleksandrovich 1 Ivanova, Tatyana B. 1 Karapetyan, Aleksandr Vladilenovich 1 Karpov, Aleksandr Ivanovich 1 Kashin, Boris Sergeevich 1 Kaspirovich, I. E. 1 Kholmskaya, A. G. 1 Klekovkin, Anton Vladimirovich 1 Kudryashov, Nikolaĭ Alekseevich 1 Kurakin, Leonid Gennadievich 1 Latypova, Natal’ya Vladimirovna 1 Lerman, Lev 1 Marikhin, Vladimir G. 1 Meleshko, V’yacheslav Volodymyrovych 1 Montaldi, James A. 1 Mukharlyamov, Robert Garabshevich 1 Neĭshtadt, Anatoliĭ Iserovich 1 Orlov, Dmitri O. 1 Pavlov, Alexander E. 1 Perelomov, Askold M. 1 Pivovarova, Elena Nikolaevna 1 Sedova, Julia V. 1 Simakov, N. N. 1 Stremler, Mark A. 1 Tarasov, Valery V. 1 Tenenev, Valentin Alekseevich 1 Tonkov, Evgenii Leonidovich 1 Turaev, Dmitry V. 1 Ushakov, Vladimir Nikolaevich 1 van Heijst, Gert-Jan F. 1 Vetchanin, Eugeny V. 1 Zhalnin, Alekseĭ Yur’evich all top 5 Serials 95 Regular and Chaotic Dynamics 9 Mathematical Notes 6 Russian Mathematical Surveys 6 Russian Journal of Mathematical Physics 5 Celestial Mechanics and Dynamical Astronomy 5 Regularnaya & Khaoticheskaya Dinamika 5 Nelineĭnaya Dinamika 4 Doklady Physics 3 Prikladnaya Matematika i Mekhanika 3 Automation and Remote Control 3 Discrete and Continuous Dynamical Systems 3 Doklady Mathematics 3 Proceedings of the Steklov Institute of Mathematics 2 Nonlinearity 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Nonlinear Dynamics 2 Theoretical and Applied Mechanics 2 Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp’yuternye Nauki 1 Acta Mechanica 1 European Journal of Physics 1 Journal of Mathematical Physics 1 Fluid Dynamics Research 1 Sibirskiĭ Matematicheskiĭ Zhurnal 1 Applied Mathematical Modelling 1 Doklady Akademii Nauk 1 Journal of Computer and Systems Sciences International 1 Chaos 1 Communications in Nonlinear Science and Numerical Simulation 1 Discrete and Continuous Dynamical Systems. Series B 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 IUTAM Bookseries 1 De Gruyter Studies in Mathematical Physics 1 Journal of Applied Nonlinear Dynamics 1 Russian Journal of Nonlinear Dynamics all top 5 Fields 139 Mechanics of particles and systems (70-XX) 123 Dynamical systems and ergodic theory (37-XX) 43 Fluid mechanics (76-XX) 9 History and biography (01-XX) 8 Ordinary differential equations (34-XX) 8 Mechanics of deformable solids (74-XX) 6 General and overarching topics; collections (00-XX) 6 Differential geometry (53-XX) 5 Systems theory; control (93-XX) 4 Partial differential equations (35-XX) 3 Probability theory and stochastic processes (60-XX) 2 Numerical analysis (65-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Computer science (68-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 158 Publications have been cited 2,059 times in 682 Documents Cited by ▼ Year ▼ Dynamics of a rigid body. Hamiltonian methods, integrability, chaos. 2nd ed. (Динамика твердого тела. Гамильтоновы методы, интегрируемость, хаос.) Zbl 1114.70001Borisov, A. V.; Mamaev, I. S. 79 2005 Rolling of a rigid body on a plane and sphere. Hierarchy of dynamics. Zbl 1058.70009Borisov, A. V.; Mamaev, I. S. 66 2002 Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems. Zbl 1229.70038Borisov, A. V.; Mamaev, I. S. 65 2008 Rolling of a ball on a surface. New integrals and hierarchy of dynamics. Zbl 1058.70010Borisov, A. V.; Mamaev, I. S.; Kilin, A. A. 56 2002 The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere. Zbl 1367.70007Borisov, Alexey V.; Mamaev, Ivan S.; Bizyaev, Ivan A. 53 2013 How to control Chaplygin’s sphere using rotors. Zbl 1264.37016Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 47 2012 Dynamics of rigid body. (Динамика твердого тела.) Zbl 1004.70002Borisov, A. V.; Mamaev, I. S. 44 2001 Topology and stability of integrable systems. Zbl 1202.37077Bolsinov, A. V.; Borisov, A. V.; Mamaev, I. S. 38 2010 Chaplygin’s ball rolling problem is Hamiltonian. Zbl 1030.70002Borisov, A. V.; Mamaev, I. S. 38 2001 How to control the Chaplygin ball using rotors. II. Zbl 1303.37021Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 37 2013 The problem of drift and recurrence for the rolling Chaplygin ball. Zbl 1286.70007Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 35 2013 The reversal and chaotic attractor in the nonholonomic model of Chaplygin’s top. Zbl 1358.70006Borisov, Alexey V.; Kazakov, Alexey O.; Sataev, Igor R. 35 2014 Dynamical phenomena occurring due to phase volume compression in nonholonomic model of the rattleback. Zbl 1263.74021Borisov, Alexey V.; Jalnine, Alexey Yu.; Kuznetsov, Sergey P.; Sataev, Igor R.; Sedova, Julia V. 33 2012 Hamiltonization of non-holonomic systems in the neighborhood of invariant manifolds. Zbl 1309.37049Bolsinov, A. V.; Borisov, A. V.; Mamaev, I. S. 31 2011 Two-body problem on a sphere. Reduction, stochasticity, periodic orbits. Zbl 1065.37058Borisov, A. V.; Mamaev, I. S.; Kilin, A. A. 30 2004 Symmetries and reduction in nonholonomic mechanics. Zbl 1342.37001Borisov, Alexey V.; Mamaev, Ivan S. 30 2015 Chaplygin ball over a fixed sphere: an explicit integration. Zbl 1229.37080Borisov, A. V.; Fedorov, Yu. N.; Mamaev, I. S. 29 2008 The Jacobi integral in nonholonomic mechanics. Zbl 1367.70036Borisov, Alexey V.; Mamaev, Ivan. S.; Bizyaev, Ivan. A. 28 2015 Compatible Poisson brackets on Lie algebras. Zbl 1042.37041Bolsinov, A. V.; Borisov, A. V. 28 2002 Mathematical methods in dynamics of vortex structures. (Математические методы динамики вихревых структур.) Zbl 1119.76001Borisov, A. V.; Mamaev, I. S. 27 2005 Asymptotic stability and associated problems of dynamics of falling rigid body. Zbl 1229.37107Borisov, A. V.; Kozlov, V. V.; Mamaev, I. S. 26 2007 On the motion of a heavy rigid body in an ideal fluid with circulation. Zbl 1144.37324Borisov, Alexey V.; Mamaev, Ivan S. 25 2006 Isomorphism and Hamilton representation of some nonholonomic systems. Zbl 1164.37342Borisov, A. V.; Mamaev, I. S. 24 2007 Poisson structures and Lie algebras in Hamiltonian mechanics. (Пуассоновы структуры и алгебры Ли в гамильтоновой механике.) Zbl 1010.70002Borisov, A. V.; Mamaev, I. S. 24 1999 The dynamics of nonholonomic systems consisting of a spherical shell with a moving rigid body inside. Zbl 1308.70003Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 23 2014 The Chaplygin sleigh with parametric excitation: chaotic dynamics and nonholonomic acceleration. Zbl 1398.37056Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 23 2017 Hamiltonicity and integrability of the Suslov problem. Zbl 1277.70008Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 22 2011 Dynamic interaction of point vortices and a two-dimensional cylinder. Zbl 1144.81318Borisov, Alexey V.; Mamaev, Ivan S.; Ramodanov, Sergey M. 22 2007 Dynamics and statics of vortices on a plane and a sphere. I. Zbl 0934.76014Borisov, A. V.; Pavlov, A. E. 22 1998 Modern methods in the theory of integrable systems. Bi-Hamiltonian description, Lax representation, and separation of variables. (Современные методы теории интегрируемых систем. Бигамильтоново описание, представление Лакса, разделение переменных.) Zbl 1101.37041Borisov, A. V.; Mamaev, I. S. 22 2003 Dynamics of rolling disk. Zbl 1112.37320Borisov, A. V.; Mamaev, I. S.; Kilin, A. A. 22 2003 Topological analysis of an integrable system related to the rolling of a ball on a sphere. Zbl 1334.37059Borisov, Alexey V.; Mamaev, Ivan S. 21 2013 Rolling of a ball without spinning on a plane: the absence of an invariant measure in a system with a complete set of integrals. Zbl 1267.37066Bolsinov, Alexey V.; Borisov, Alexey V.; Mamaev, Ivan S. 20 2012 Geometrisation of Chaplygin’s reducing multiplier theorem. Zbl 1333.37103Bolsinov, A. V.; Borisov, A. V.; Mamaev, I. S. 20 2015 Generalized Chaplygin’s transformation and explicit integration of a system with a spherical support. Zbl 1253.37063Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 19 2012 Non-holonomic dynamics and Poisson geometry. Zbl 1348.70038Borisov, A. V.; Mamaev, I. S.; Tsiganov, A. V. 19 2014 An integrability of the problem on motion of cylinder and vortex in the ideal fluid. Zbl 1112.37315Borisov, A. V.; Mamaev, I. S. 19 2003 Motion of a circular cylinder and \(n\) point vortices in a perfect fluid. Zbl 1051.76009Borisov, A. V.; Mamaev, I. S.; Ramodanov, S. M. 18 2003 On the Hadamard-Hamel problem and the dynamics of wheeled vehicles. Zbl 1367.70034Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 17 2015 Stability of Thomson’s configurations of vortices on a sphere. Zbl 0967.76023Borisov, A. V.; Kilin, A. A. 17 2000 The restricted two-body problem in constant curvature spaces. Zbl 1116.70015Borisov, Alexey V.; Mamaev, Ivan S. 17 2006 Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors. Zbl 1344.37073Bizyaev, Ivan A.; Borisov, Alexey V.; Kazakov, Alexey O. 17 2015 New effects in dynamics of rattlebacks. Zbl 1206.70007Borisov, A. V.; Kilin, A. A.; Mamaev, I. S. 16 2006 Multiparticle systems. The algebra of integrals and integrable cases. Zbl 1229.37106Borisov, A. V.; Kilin, A. A.; Mamaev, I. S. 16 2009 Rolling of a non-homogeneous ball over a sphere without slipping and twisting. Zbl 1229.37081Borisov, A. V.; Mamaev, I. S. 16 2007 The spatial problem of 2 bodies on a sphere. Reduction and stochasticity. Zbl 1402.70015Borisov, Alexey V.; Mamaev, Ivan S.; Bizyaev, Ivan A. 16 2016 The Hess case in rigid-body dynamics. Zbl 1066.70504Borisov, A. V.; Mamayev, I. S. 15 2003 Absolute and relative choreographies in the problem of point vortices moving on a plane. Zbl 1079.76020Borisov, A. V.; Mamaev, I. S.; Kilin, A. A. 15 2004 Dynamics of three vortices on a plane and a sphere. II: General compact case. Zbl 0933.76016Borisov, A. V.; Lebedev, V. G. 15 1998 Lie algebras in vortex dynamics and celestial mechanics. IV. Zbl 1076.76513Bolsinov, A. V.; Borisov, A. V.; Mamaev, I. S. 15 1999 Exotic dynamics of nonholonomic roller racer with periodic control. Zbl 1412.37064Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 15 2018 On the problem of motion of vortex sources on a plane. Zbl 1164.37353Borisov, A. V.; Mamaev, I. S. 14 2006 Dynamics and control of an omniwheel vehicle. Zbl 1367.70033Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 14 2015 Generalized problem of two and four Newtonian centers. Zbl 1129.70010Borisov, Alexey V.; Mamaev, Ivan S. 14 2005 Paul Painlevé and his contribution to science. Zbl 1333.01025Borisov, Alexey V.; Kudryashov, Nikolay A. 14 2014 The dynamics of vortex rings: leapfrogging, choreographies and the stability problem. Zbl 1273.76067Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 13 2013 Relations between integrable systems in plane and curved spaces. Zbl 1202.70062Borisov, Alexey V.; Mamaev, Ivan S. 13 2007 Fermi-like acceleration and power-law energy growth in nonholonomic systems. Zbl 1418.37106Bizyaev, I. A.; Borisov, A. V.; Kozlov, V. V.; Mamaev, I. S. 13 2019 Qualitative analysis of the dynamics of a wheeled vehicle. Zbl 1367.70035Borisov, Alexey V.; Mamaev, Ivan S.; Kilin, Alexander A.; Bizyaev, Ivan A. 12 2015 Bifurcation analysis and the Conley index in mechanics. Zbl 1252.76055Bolsinov, Alexey V.; Borisov, Alexey V.; Mamaev, Ivan S. 12 2012 Regular and chaotic motions of a Chaplygin sleigh under periodic pulsed torque impacts. Zbl 1368.37075Borisov, Alexey V.; Kuznetsov, Sergey P. 12 2016 Superintegrable systems on a sphere. Zbl 1077.37520Borisov, A. V.; Mamaev, I. S. 12 2005 Rolling of a homogeneous ball over a dynamically asymmetric sphere. Zbl 1309.37080Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 12 2011 The dynamics of three vortex sources. Zbl 1342.37078Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 12 2014 Historical and critical review of the development of nonholonomic mechanics: the classical period. Zbl 1352.37172Borisov, Alexey V.; Mamaev, Ivan S.; Bizyaev, Ivan A. 12 2016 Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics. Zbl 1446.70034Borisov, Alexey V.; Mamaev, Ivan S.; Bizyaev, Ivan A. 12 2017 Two non-holonomic integrable problems tracing back to Chaplygin. Zbl 1252.76056Borisov, Alexey V.; Mamaev, Ivan S. 10 2012 Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups. Zbl 1367.53030Bizyaev, Ivan Alekseevich; Borisov, Alekseĭ Vladimirovich; Kilin, Aleksandr Aleksandrovich; Mamaev, Ivan Sergeevich 10 2016 Spiral chaos in the nonholonomic model of a Chaplygin top. Zbl 1378.37112Borisov, Alexey V.; Kazakov, Alexey O.; Sataev, Igor R. 10 2016 The Hamiltonian dynamics of self-gravitating liquid and gas ellipsoids. Zbl 1229.70049Borisov, A. V.; Kilin, A. A.; Mamaev, I. S. 10 2009 Topology and bifurcations in nonholonomic mechanics. Zbl 1326.70022Bizyaev, Ivan A.; Bolsinov, Alexey; Borisov, Alexey; Mamaev, Ivan 10 2015 Regular and chaotic dynamics in the rubber model of a Chaplygin top. Zbl 1368.37074Borisov, Alexey V.; Kazakov, Alexey O.; Pivovarova, Elena N. 9 2016 Superintegrable system on a sphere with the integral of higher degree. Zbl 1229.70052Borisov, A. V.; Kilin, A. A.; Mamaev, I. S. 9 2009 Rolling of a rigid body without slipping and spinning: kinematics and dynamics. Zbl 1367.70006Borisov, A. V.; Mamaev, I. S.; Treschev, D. V. 9 2013 On the history of the development of the nonholonomic dynamics. Zbl 1011.70002Borisov, A. V.; Mamaev, I. S. 9 2002 Superintegrable generalizations of the Kepler and Hook problems. Zbl 1309.70020Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 9 2014 Reduction and chaotic behavior of point vortices on a plane and a sphere. Zbl 1144.37458Borisov, A. V.; Kilin, A. A.; Mamaev, I. S. 8 2005 Dynamics of the Chaplygin sledge. Zbl 1183.74080Borisov, A. V.; Mamayev, I. S. 8 2009 The dynamics of the Chaplygin ball with a fluid-filled cavity. Zbl 1286.70008Borisov, Alexey V.; Mamaev, Ivan S. 8 2013 The dynamics of a body with an axisymmetric base sliding on a rough plane. Zbl 1353.70038Borisov, Alexey V.; Erdakova, Nadezhda N.; Ivanova, Tatiana B.; Mamaev, Ivan S. 8 2014 Experimental investigation of the motion of a body with an axisymmetric base sliding on a rough plane. Zbl 1343.70017Borisov, Alexey V.; Karavaev, Yury L.; Mamaev, Ivan S.; Erdakova, Nadezhda N.; Ivanova, Tatyana B.; Tarasov, Valery V. 8 2015 Bifurcation analysis of the motion of a cylinder and a point vortex in an ideal fluid. Zbl 1404.37065Borisov, A. V.; Ryabov, P. E.; Sokolov, S. V. 8 2016 The Hess-Appelrot system and its nonholonomic analogs. Zbl 1404.70034Bizyaev, I. A.; Borisov, A. V.; Mamaev, I. S. 8 2016 The dynamics of vortex sources in a deformation flow. Zbl 1346.76118Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 8 2016 Control of the motion of a triaxial ellipsoid in a fluid using rotors. Zbl 1382.37089Borisov, A. V.; Vetchanin, E. V.; Kilin, A. A. 8 2017 Self-propulsion of a smooth body in a viscous fluid under periodic oscillations of a rotor and circulation. Zbl 1412.37076Borisov, Alexey V.; Mamaev, Ivan S.; Vetchanin, Evgeny V. 8 2018 Hamiltonization of elementary nonholonomic systems. Zbl 1360.70022Bizyaev, I. A.; Borisov, A. V.; Mamaev, I. S. 7 2015 Rigid body dynamics in non-Euclidean spaces. Zbl 1406.70009Borisov, A. V.; Mamaev, I. S. 7 2016 Explicit integration of one problem in nonholonomic mechanics. Zbl 1206.70011Borisov, A. V.; Mamaev, I. S.; Marikhin, V. G. 7 2008 Dynamics of three vortices on a plane and a sphere. III: Noncompact case. Problems of collapse and scattering. Zbl 0958.76013Borisov, A. V.; Lebedev, V. G. 7 1998 Kovalevskaya exponents and Poisson structures. Zbl 1012.37032Borisov, A. V.; Dudoladov, S. L. 7 1999 Necessary and sufficient conditions for integrability of the Kirchhoff equations. Zbl 1001.70501Borisov, A. V. 7 1996 Dynamics of a smooth profile in a medium with friction in the presence of parametric excitation. Zbl 1411.70027Borisov, Alexey V.; Mamaev, Ivan S.; Vetchanin, Eugeny V. 7 2018 Comparing dynamics initiated by an attached oscillating particle for the nonholonomic model of a Chaplygin sleigh and for a model with strong transverse and weak longitudinal viscous friction applied at a fixed point on the body. Zbl 1412.37065Borisov, Alexey V.; Kuznetsov, Sergey P. 7 2018 Reduction and relative equilibria for the two-body problem on spaces of constant curvature. Zbl 1396.70011Borisov, A. V.; García-Naranjo, L. C.; Mamaev, I. S.; Montaldi, J. 7 2018 Dynamics of the Chaplygin sleigh on a cylinder. Zbl 1346.70006Bizyaev, Ivan Alekseevich; Borisov, Alekseĭ Vladimirovich; Mamaev, Ivan Sergeevich 6 2016 Stability of steady rotations in the nonholonomic Routh problem. Zbl 1229.70021Borisov, A. V.; Kilin, A. A.; Mamaev, I. S. 6 2008 Isomorphisms of geodesic flows on quadrics. Zbl 1229.37096Borisov, A. V.; Mamaev, I. S. 6 2009 The nonexistence of an invariant measure for an inhomogeneous ellipsoid rolling on a plane. Zbl 1081.37539Borisov, A. V.; Mamaev, I. S. 6 2005 Adiabatic chaos in rigid body dynamics. Zbl 0933.70007Borisov, A. V.; Mamaev, I. S. 6 1997 On inhomogeneous nonholonomic Bilimovich system. Zbl 1455.37053Borisov, A. V.; Tsiganov, A. V.; Mikishanina, E. A. 1 2021 Dynamics of the tippe top on a vibrating base. Zbl 1475.70007Borisov, Alexey V.; Ivanov, Alexander P. 3 2020 Dynamics of multi-link uncontrolled wheeled vehicle. Zbl 1468.70003Borisov, A. V.; Mikishanina, E. A.; Sokolov, S. V. 2 2020 On the existence of focus singularities in one model of a Lagrange top with a vibrating suspension point. Zbl 1482.37054Borisov, A. V.; Ryabov, P. E.; Sokolov, S. V. 1 2020 On the stability of a system of two identical point vortices and a cylinder. Zbl 1459.76055Borisov, A. V.; Kurakin, L. G. 1 2020 Fermi-like acceleration and power-law energy growth in nonholonomic systems. Zbl 1418.37106Bizyaev, I. A.; Borisov, A. V.; Kozlov, V. V.; Mamaev, I. S. 13 2019 Rigid body dynamics. Zbl 1450.70001Borisov, Alexey V.; Mamaev, Ivan S. 6 2019 Invariant submanifolds of genus 5 and a Cantor staircase in the nonholonomic model of a snakeboard. Zbl 1411.70022Borisov, Alexey; Kilin, Alexander; Mamaev, Ivan 5 2019 Nonholonomic rolling of a ball on the surface of a rotating cone. Zbl 1430.37068Borisov, Alexey V.; Ivanova, Tatiana B.; Kilin, Alexander A.; Mamaev, Ivan S. 4 2019 Different models of rolling for a robot ball on a plane as a generalization of the Chaplygin ball problem. Zbl 1437.37078Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 4 2019 On the Chaplygin sphere in a magnetic field. Zbl 1435.37093Borisov, Alexey V.; Tsiganov, Andrey V. 2 2019 Motion of a smooth foil in a fluid under the action of external periodic forces. I. Zbl 1448.74030Borisov, A. V.; Vetchanin, E. V.; Mamaev, I. S. 2 2019 Stabilization of the motion of a spherical robot using feedbacks. Zbl 1443.70024Borisov, Alexey; Kilin, Alexander; Karavaev, Yury; Klekovkin, Anton 2 2019 Exotic dynamics of nonholonomic roller racer with periodic control. Zbl 1412.37064Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 15 2018 Self-propulsion of a smooth body in a viscous fluid under periodic oscillations of a rotor and circulation. Zbl 1412.37076Borisov, Alexey V.; Mamaev, Ivan S.; Vetchanin, Evgeny V. 8 2018 Dynamics of a smooth profile in a medium with friction in the presence of parametric excitation. Zbl 1411.70027Borisov, Alexey V.; Mamaev, Ivan S.; Vetchanin, Eugeny V. 7 2018 Comparing dynamics initiated by an attached oscillating particle for the nonholonomic model of a Chaplygin sleigh and for a model with strong transverse and weak longitudinal viscous friction applied at a fixed point on the body. Zbl 1412.37065Borisov, Alexey V.; Kuznetsov, Sergey P. 7 2018 Reduction and relative equilibria for the two-body problem on spaces of constant curvature. Zbl 1396.70011Borisov, A. V.; García-Naranjo, L. C.; Mamaev, I. S.; Montaldi, J. 7 2018 Dynamics of the Chaplygin ball on a rotating plane. Zbl 1435.70017Bizyaev, I. A.; Borisov, A. V.; Mamaev, I. S. 6 2018 Theoretical and experimental investigations of the rolling of a ball on a rotating plane (turntable). Zbl 1421.70011Borisov, Alexey V.; Ivanova, Tatiana B.; Karavaev, Yury L.; Mamaev, Ivan S. 4 2018 A nonholonomic model of the Paul trap. Zbl 1400.37075Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 4 2018 Three vortices in spaces of constant curvature: reduction, Poisson geometry, and stability. Zbl 1411.76116Borisov, Alexey V.; Mamaev, Ivan S.; Bizyaev, Ivan A. 3 2018 An invariant measure and the probability of a fall in the problem of an inhomogeneous disk rolling on a plane. Zbl 1410.37059Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 2 2018 Dynamics of three vortices on a sphere. Zbl 1400.76055Borisov, Alexey V.; Mamaev, Ivan S.; Kilin, Alexander A. 2 2018 The Chaplygin sleigh with parametric excitation: chaotic dynamics and nonholonomic acceleration. Zbl 1398.37056Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 23 2017 Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics. Zbl 1446.70034Borisov, Alexey V.; Mamaev, Ivan S.; Bizyaev, Ivan A. 12 2017 Control of the motion of a triaxial ellipsoid in a fluid using rotors. Zbl 1382.37089Borisov, A. V.; Vetchanin, E. V.; Kilin, A. A. 8 2017 The Hess-Appelrot case and quantization of the rotation number. Zbl 1370.70023Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 6 2017 An inhomogeneous Chaplygin sleigh. Zbl 1404.37073Borisov, Alexey V.; Mamaev, Ivan S. 6 2017 The spatial problem of 2 bodies on a sphere. Reduction and stochasticity. Zbl 1402.70015Borisov, Alexey V.; Mamaev, Ivan S.; Bizyaev, Ivan A. 16 2016 Regular and chaotic motions of a Chaplygin sleigh under periodic pulsed torque impacts. Zbl 1368.37075Borisov, Alexey V.; Kuznetsov, Sergey P. 12 2016 Historical and critical review of the development of nonholonomic mechanics: the classical period. Zbl 1352.37172Borisov, Alexey V.; Mamaev, Ivan S.; Bizyaev, Ivan A. 12 2016 Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups. Zbl 1367.53030Bizyaev, Ivan Alekseevich; Borisov, Alekseĭ Vladimirovich; Kilin, Aleksandr Aleksandrovich; Mamaev, Ivan Sergeevich 10 2016 Spiral chaos in the nonholonomic model of a Chaplygin top. Zbl 1378.37112Borisov, Alexey V.; Kazakov, Alexey O.; Sataev, Igor R. 10 2016 Regular and chaotic dynamics in the rubber model of a Chaplygin top. Zbl 1368.37074Borisov, Alexey V.; Kazakov, Alexey O.; Pivovarova, Elena N. 9 2016 Bifurcation analysis of the motion of a cylinder and a point vortex in an ideal fluid. Zbl 1404.37065Borisov, A. V.; Ryabov, P. E.; Sokolov, S. V. 8 2016 The Hess-Appelrot system and its nonholonomic analogs. Zbl 1404.70034Bizyaev, I. A.; Borisov, A. V.; Mamaev, I. S. 8 2016 The dynamics of vortex sources in a deformation flow. Zbl 1346.76118Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 8 2016 Rigid body dynamics in non-Euclidean spaces. Zbl 1406.70009Borisov, A. V.; Mamaev, I. S. 7 2016 Dynamics of the Chaplygin sleigh on a cylinder. Zbl 1346.70006Bizyaev, Ivan Alekseevich; Borisov, Alekseĭ Vladimirovich; Mamaev, Ivan Sergeevich 6 2016 The Hojman construction and hamiltonization of nonholonomic systems. Zbl 1331.37087Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 4 2016 Adiabatic invariants, diffusion and acceleration in rigid body dynamics. Zbl 1377.70021Borisov, Alexey V.; Mamaev, Ivan S. 3 2016 Dynamics of a body sliding on a rough plane and supported at three points. Zbl 1474.70019Borisov, Alexey V.; Mamaev, Ivan S.; Erdakova, Nadezhda N. 1 2016 Symmetries and reduction in nonholonomic mechanics. Zbl 1342.37001Borisov, Alexey V.; Mamaev, Ivan S. 30 2015 The Jacobi integral in nonholonomic mechanics. Zbl 1367.70036Borisov, Alexey V.; Mamaev, Ivan. S.; Bizyaev, Ivan. A. 28 2015 Geometrisation of Chaplygin’s reducing multiplier theorem. Zbl 1333.37103Bolsinov, A. V.; Borisov, A. V.; Mamaev, I. S. 20 2015 On the Hadamard-Hamel problem and the dynamics of wheeled vehicles. Zbl 1367.70034Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 17 2015 Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors. Zbl 1344.37073Bizyaev, Ivan A.; Borisov, Alexey V.; Kazakov, Alexey O. 17 2015 Dynamics and control of an omniwheel vehicle. Zbl 1367.70033Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 14 2015 Qualitative analysis of the dynamics of a wheeled vehicle. Zbl 1367.70035Borisov, Alexey V.; Mamaev, Ivan S.; Kilin, Alexander A.; Bizyaev, Ivan A. 12 2015 Topology and bifurcations in nonholonomic mechanics. Zbl 1326.70022Bizyaev, Ivan A.; Bolsinov, Alexey; Borisov, Alexey; Mamaev, Ivan 10 2015 Experimental investigation of the motion of a body with an axisymmetric base sliding on a rough plane. Zbl 1343.70017Borisov, Alexey V.; Karavaev, Yury L.; Mamaev, Ivan S.; Erdakova, Nadezhda N.; Ivanova, Tatyana B.; Tarasov, Valery V. 8 2015 Hamiltonization of elementary nonholonomic systems. Zbl 1360.70022Bizyaev, I. A.; Borisov, A. V.; Mamaev, I. S. 7 2015 Figures of equilibrium of an inhomogeneous self-gravitating fluid. Zbl 1409.76146Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 3 2015 Equations of motion of non-holonomic systems. Zbl 1343.37054Borisov, A. V.; Mamaev, I. S. 2 2015 The reversal and chaotic attractor in the nonholonomic model of Chaplygin’s top. Zbl 1358.70006Borisov, Alexey V.; Kazakov, Alexey O.; Sataev, Igor R. 35 2014 The dynamics of nonholonomic systems consisting of a spherical shell with a moving rigid body inside. Zbl 1308.70003Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 23 2014 Non-holonomic dynamics and Poisson geometry. Zbl 1348.70038Borisov, A. V.; Mamaev, I. S.; Tsiganov, A. V. 19 2014 Paul Painlevé and his contribution to science. Zbl 1333.01025Borisov, Alexey V.; Kudryashov, Nikolay A. 14 2014 The dynamics of three vortex sources. Zbl 1342.37078Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 12 2014 Superintegrable generalizations of the Kepler and Hook problems. Zbl 1309.70020Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 9 2014 The dynamics of a body with an axisymmetric base sliding on a rough plane. Zbl 1353.70038Borisov, Alexey V.; Erdakova, Nadezhda N.; Ivanova, Tatiana B.; Mamaev, Ivan S. 8 2014 The dynamics of vortex rings: leapfrogging in an ideal and viscous fluid. Zbl 1307.76036Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S.; Tenenev, Valentin A. 5 2014 On the dynamics of a body with an axisymmetric base sliding on a rough plane. Zbl 1353.70037Borisov, Alexey V.; Erdakova, Nadezhda N.; Ivanova, Tatiana B.; Mamaev, Ivan S. 2 2014 Figures of equilibrium of an inhomogeneous self-gravitating fluid. Zbl 1310.76175Bizyaev, Ivan A.; Borisov, Alexey V.; Mamaev, Ivan S. 1 2014 On the nonlinear Poisson bracket arising in nonholonomic mechanics. Zbl 1348.70039Borisov, A. V.; Mamaev, I. S.; Tsyganov, A. V. 1 2014 The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere. Zbl 1367.70007Borisov, Alexey V.; Mamaev, Ivan S.; Bizyaev, Ivan A. 53 2013 How to control the Chaplygin ball using rotors. II. Zbl 1303.37021Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 37 2013 The problem of drift and recurrence for the rolling Chaplygin ball. Zbl 1286.70007Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 35 2013 Topological analysis of an integrable system related to the rolling of a ball on a sphere. Zbl 1334.37059Borisov, Alexey V.; Mamaev, Ivan S. 21 2013 The dynamics of vortex rings: leapfrogging, choreographies and the stability problem. Zbl 1273.76067Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 13 2013 Rolling of a rigid body without slipping and spinning: kinematics and dynamics. Zbl 1367.70006Borisov, A. V.; Mamaev, I. S.; Treschev, D. V. 9 2013 The dynamics of the Chaplygin ball with a fluid-filled cavity. Zbl 1286.70008Borisov, Alexey V.; Mamaev, Ivan S. 8 2013 How to control Chaplygin’s sphere using rotors. Zbl 1264.37016Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 47 2012 Dynamical phenomena occurring due to phase volume compression in nonholonomic model of the rattleback. Zbl 1263.74021Borisov, Alexey V.; Jalnine, Alexey Yu.; Kuznetsov, Sergey P.; Sataev, Igor R.; Sedova, Julia V. 33 2012 Rolling of a ball without spinning on a plane: the absence of an invariant measure in a system with a complete set of integrals. Zbl 1267.37066Bolsinov, Alexey V.; Borisov, Alexey V.; Mamaev, Ivan S. 20 2012 Generalized Chaplygin’s transformation and explicit integration of a system with a spherical support. Zbl 1253.37063Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 19 2012 Bifurcation analysis and the Conley index in mechanics. Zbl 1252.76055Bolsinov, Alexey V.; Borisov, Alexey V.; Mamaev, Ivan S. 12 2012 Two non-holonomic integrable problems tracing back to Chaplygin. Zbl 1252.76056Borisov, Alexey V.; Mamaev, Ivan S. 10 2012 Hamiltonization of non-holonomic systems in the neighborhood of invariant manifolds. Zbl 1309.37049Bolsinov, A. V.; Borisov, A. V.; Mamaev, I. S. 31 2011 Hamiltonicity and integrability of the Suslov problem. Zbl 1277.70008Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 22 2011 Rolling of a homogeneous ball over a dynamically asymmetric sphere. Zbl 1309.37080Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 12 2011 On the model of non-holonomic billiard. Zbl 1253.70008Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 2 2011 Hassan Aref (1950–2011). Zbl 1253.01021Borisov, Alexey V.; Meleshko, Viatcheslav V.; Stremler, Mark; van Heijst, GertJan 1 2011 Topology and stability of integrable systems. Zbl 1202.37077Bolsinov, A. V.; Borisov, A. V.; Mamaev, I. S. 38 2010 Coupled motion of a rigid body and point vortices on a two-dimensional spherical surface. Zbl 1258.76050Borisov, A. V.; Mamaev, I. S.; Ramodanov, S. M. 3 2010 Basic principles and models of dynamic advection. Zbl 1337.76069Borisov, A. V.; Mamaev, I. S.; Ramodanov, S. M. 2 2010 Multiparticle systems. The algebra of integrals and integrable cases. Zbl 1229.37106Borisov, A. V.; Kilin, A. A.; Mamaev, I. S. 16 2009 The Hamiltonian dynamics of self-gravitating liquid and gas ellipsoids. Zbl 1229.70049Borisov, A. V.; Kilin, A. A.; Mamaev, I. S. 10 2009 Superintegrable system on a sphere with the integral of higher degree. Zbl 1229.70052Borisov, A. V.; Kilin, A. A.; Mamaev, I. S. 9 2009 Dynamics of the Chaplygin sledge. Zbl 1183.74080Borisov, A. V.; Mamayev, I. S. 8 2009 Isomorphisms of geodesic flows on quadrics. Zbl 1229.37096Borisov, A. V.; Mamaev, I. S. 6 2009 Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems. Zbl 1229.70038Borisov, A. V.; Mamaev, I. S. 65 2008 Chaplygin ball over a fixed sphere: an explicit integration. Zbl 1229.37080Borisov, A. V.; Fedorov, Yu. N.; Mamaev, I. S. 29 2008 Explicit integration of one problem in nonholonomic mechanics. Zbl 1206.70011Borisov, A. V.; Mamaev, I. S.; Marikhin, V. G. 7 2008 Stability of steady rotations in the nonholonomic Routh problem. Zbl 1229.70021Borisov, A. V.; Kilin, A. A.; Mamaev, I. S. 6 2008 A new integrable problem of motion of point vortices on the sphere. Zbl 1207.76030Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S. 4 2008 Absolute and relative choreographies in rigid body dynamics. Zbl 1229.70009Borisov, A. V.; Kilin, A. A.; Mamaev, I. S. 2 2008 Chaos in a restricted problem of rotation of a rigid body with a fixed point. Zbl 1229.70011Borisov, A. V.; Kilin, A. A.; Mamaev, I. S. 2 2008 Dynamics of two rings of vortices on a sphere. Zbl 1207.76031Borisov, Alexey V.; Mamaev, Ivan S. 2 2008 ...and 58 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 549 Authors 107 Borisov, Alekseĭ Vladimirovich 95 Mamaev, Ivan Sergeevich 48 Kilin, Aleksandr Aleksandrovich 34 Bizyaev, Ivan Alekseevich 31 Tsyganov, Andreĭ Vladimirovich 21 Kudryashov, Nikolaĭ Alekseevich 18 Vetchanin, Evgeniĭ Vladimirovich 17 García-Naranjo, Luis C. 15 Kazakov, Alexey O. 13 Ryabov, Pavel Evgen’evich 12 Pivovarova, Elena Nikolaevna 12 Przybylska, Maria 12 Sokolov, Sergeĭ Viktorovich 11 Bolsinov, Alexey V. 11 Karavaev, Yurĭ Leonidovich 11 Kurakin, Leonid Gennadievich 10 Dragović, Vladimir 10 Maciejewski, Andrzej J. 9 Kozlov, Valeriĭ Vasil’evich 9 Kuznetsov, Sergey P. 8 Gajić, Borislav 8 Gonchenko, Alexander S. 8 Mikishanina, Evgeniya Arifzhanovna 7 Balseiro, Paula 7 Gonchenko, Sergey V. 6 Bloch, Anthony Michael 6 Gorr, Gennadiĭ Viktorovich 6 Montaldi, James A. 6 Ostrovskaya, Irina V. 5 Albouy, Alain 5 Fernandez, Oscar E. 5 Ivanov, Aleksandr Pavlovich 5 Ivanova, Tatiana B. 5 Ivanova, Tatyana B. 5 Jovanović, Božidar Žarko 5 Kanso, Eva Adnan 5 Marrero, Juan Carlos 5 Newton, Paul K. 5 Ol’shanskii, V. Yu. 5 Pérez-Chavela, Ernesto 5 Ramodanov, Sergey M. 5 Sansonetto, Nicola 5 Sinelshchikov, Dmitry I. 5 Stremler, Mark A. 5 Tenenev, Valentin Alekseevich 4 Bardin, Boris Sabirovich 4 Cendra, Hernán 4 Damianou, Pantelis Andrea 4 Dobrogowska, Alina 4 Fassò, Francesco 4 Koiller, Jair 4 Lăzureanu, Cristian 4 Llibre, Jaume 4 Markeev, Anatoliĭ Pavlovich 4 Oshemkov, Andreĭ Aleksandrovich 4 Popov, Sasho Ivanov 4 Putkaradze, Vakhtang 4 Rañada, Manuel F. 4 Rauch-Wojciechowski, Stefan 4 Sataev, Igor’ Rustamovich 4 Shashikanth, Banavara N. 4 Sokolovskiy, Mikhail A. 4 Tallapragada, Phanindra 4 Zhu, Shuqiang 4 Zobova, Alexandra A. 3 Akbarzadeh, Rasoul 3 Andrade, Jaime 3 Aref, Hassan 3 Artemova, Elizaveta M. 3 Bolotin, Sergeĭ Vladimirovich 3 Burov, Aleksandr Anatol’evich 3 Cariñena, José F. 3 Combot, Thierry 3 Demina, Maria V. 3 Dritschel, David Gerard 3 Elmandouh, Adel A. 3 Erdakova, Nadezhda N. 3 Fedonyuk, Vitaliy 3 Fedorov, Yuri N. 3 García-Azpeitia, Carlos 3 Gebhard, Björn 3 Grishanina, G. É. 3 Gudimenko, A. I. 3 Inozemtseva, Natalia G. 3 Kelly, Scott David 3 Kharlamov, Mikhail Pavlovich 3 Klekovkin, Anton Vladimirovich 3 Konyaev, Andreĭ Yu. 3 Llewellyn Smith, Stefan G. 3 Mityushov, Evgeniĭ Aleksandrovich 3 Sachkov, Yuriĭ Leonidovich 3 Sánchez-Cerritos, Juan Manuel 3 Santander, Mariano 3 Strelcyn, Jean-Marie 3 Svinin, Mikhail M. 3 Turaev, Dmitry V. 3 Vankerschaver, Joris 3 Yamamoto, Motoji 3 Zhila, A. I. 2 Amer, Tarek S. ...and 449 more Authors all top 5 Cited in 104 Serials 246 Regular and Chaotic Dynamics 31 Russian Journal of Nonlinear Dynamics 18 Journal of Mathematical Physics 17 Journal of Nonlinear Science 14 Physica D 14 Journal of Geometric Mechanics 12 Journal of Applied Mathematics and Mechanics 12 Journal of Mathematical Sciences (New York) 11 Doklady Mathematics 10 Journal of Fluid Mechanics 10 Russian Journal of Mathematical Physics 10 Nonlinear Dynamics 10 Chaos 10 Proceedings of the Steklov Institute of Mathematics 9 Physics Letters. 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