Publications
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2022

1.A Simple Physical Model for Control of an Propellerless Aquatic Robot
Journal of Mechanisms and Robotics, 2022, vol. 14, no. 1, 011007,11 pp.
Abstract pdf (981.69 Kb)
2021

2.Qualitative Analysis of the Dynamics of a Balanced Circular Foil and a Vortex
Regular and Chaotic Dynamics, 2021, vol. 26, no. 6,pp. 658674
Abstract pdf (1.34 Mb) 
3.Normal forms and averaging in an acceleration problem in nonholonomic mechanics
Chaos, 2021, vol. 31, 013132,16 pp.
Abstract pdf (1.05 Mb) 
4.Dynamics of an unbalanced circular foil and point vortices in an ideal fluid
Physics of Fluids, 2021, vol. 33, 087119,18 pp.
Abstract pdf (2.36 Mb)
2020

5.Separatrix splitting and nonintegrability in the nonholonomic rolling of a generalized Chaplygin sphere
International Journal of NonLinear Mechanics, 2020, vol. 126, 103550,7 pp.
Abstract pdf (2.22 Mb) 
6.Dynamics of a pair of point vortices and a foil with parametric excitation in an ideal fluid
Bulletin of Udmurt University. Mathematics. Mechanics. Computer Science, 2020, vol. 30, no. 4,pp. 618627
Abstract pdf (553.19 Kb) 
7.Dynamics of a Spherical Robot with Variable Moments of Inertia and a Displaced Center of Mass
Regular and Chaotic Dynamics, 2020, vol. 25, no. 6,pp. 689706
Abstract pdf (950.79 Kb) 
8.Dynamics of Rubber Chaplygin Sphere under Periodic Control
Regular and Chaotic Dynamics, 2020, vol. 25, no. 2,pp. 215236
Abstract pdf (4.03 Mb) 
9.Circular orbits of a ball on a rotating conical turntable
Acta Mechanica, 2020, vol. 231, no. 3,pp. 1021–1028
Abstract pdf (323.69 Kb) 
10.Motion of a Smooth Foil in a Fluid under the Action of External Periodic Forces. II
Russian Journal of Mathematical Physics, 2020, vol. 27, no. 1,pp. 117
Abstract pdf (1.98 Mb) 
11.Dynamics of the nonholonomic Suslov problem under periodic control: unbounded speedup and strange attractors
Journal of Physics A: Mathematical and Theoretical, 2020, vol. 53, 185701,17 pp.
Abstract pdf (1.24 Mb) 
12.Asymptotic behavior in the dynamics of a smooth body in an ideal fluid
Acta Mechanica, 2020, vol. 231,pp. 45294535
Abstract pdf (519.06 Kb) 
13.Spherical rolling robots: Different designs and control algorithms
Robots in Human Life: Proceedings of the 23rd International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines, CLAWAR 2020, 2020,pp. 195202
Abstract pdf (415.75 Kb) 
14.Propellerless aquatic robots
Robots in Human Life: Proceedings of the 23rd International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines, CLAWAR 2020, 2020,pp. 404411
Abstract pdf (633.84 Kb) 
15.Controlled motion of a highly maneuverable mobile robot along curvilinear trajectories
2020 International Conference Nonlinearity, Information and Robotics – IEEE, 2020,pp. 14
Abstract pdf (3.15 Mb) 
16.Dynamics of a spherical robot with periodically changing moments of inertia
2020 International Conference Nonlinearity, Information and Robotics – IEEE, 2020,pp. 15
Abstract pdf (310.64 Kb) 
17.Dynamics of point vortices and a cylinder in an ideal fluid
2020 International Conference Nonlinearity, Information and Robotics – IEEE, 2020,pp. 13
Abstract pdf (241.98 Kb) 
18.Experimental evaluation of simplified physical model for control of aquatic robot with internal rotor
2020 International Conference Nonlinearity, Information and Robotics – IEEE, 2020,pp. 12
Abstract pdf (330.17 Kb)
2019

19.Different Models of Rolling for a Robot Ball on a Plane as a Generalization of the Chaplygin Ball Problem
Regular and Chaotic Dynamics, 2019, vol. 24, no. 5,pp. 560582
Abstract pdf (1.93 Mb) 
20.A Parabolic Chaplygin Pendulum and a Paul Trap: Nonintegrability, Stability, and Boundedness
Regular and Chaotic Dynamics, 2019, vol. 24, no. 3,pp. 329352
Abstract pdf (1.48 Mb) 
21.Invariant Submanifolds of Genus 5 and a Cantor Staircase in the Nonholonomic Model of a Snakeboard
International Journal of Bifurcation and Chaos, 2019, vol. 29, no. 3, 1930008,19 pp.
Abstract pdf (2.79 Mb) 
22.Fermilike acceleration and powerlaw energy growth in nonholonomic systems
Nonlinearity, 2019, vol. 32,pp. 32093233
Abstract pdf (974.09 Kb) 
23.Nonholonomic rolling of a ball on the surface of a rotating cone
Nonlinear Dynamics, 2019, vol. 97, no. 2,pp. 16351648
Abstract pdf (1.04 Mb) 
24.Comment on “Confining rigid balls by mimicking quadrupole ion trapping” [Am. J. Phys. 85, 821 (2017)]
American Journal of Physics, 2019, vol. 87, no. 11,pp. 935938
Abstract pdf (2.18 Mb) 
25.Dynamics of a Chaplygin sleigh with an unbalanced rotor: regular and chaotic motions
Nonlinear Dynamics, 2019, vol. 98,pp. 22772291
Abstract pdf (829 Kb) 
26.Motion of a Smooth Foil in a Fluid under the Action of External Periodic Forces. I
Russian Journal of Mathematical Physics, 2019, vol. 26, no. 4,pp. 412428
Abstract pdf (963.73 Kb)
2018

27.Reduction and relative equilibria for the twobody problem on spaces of constant curvature
Celestial Mechanics and Dynamical Astronomy, 2018, vol. 130, no. 6,pp. 136
Abstract pdf (1.38 Mb) 
28.Selfpropulsion of a Smooth Body in a Viscous Fluid Under Periodic Oscillations of a Rotor and Circulation
Regular and Chaotic Dynamics, 2018, vol. 23, no. 78,pp. 850874
Abstract pdf (4.03 Mb) 
29.The Selfpropulsion of a Foil with a Sharp Edge in a Viscous Fluid Under the Action of a Periodically Oscillating Rotor
Regular and Chaotic Dynamics, 2018, vol. 23, no. 78,pp. 875886
Abstract pdf (1.64 Mb) 
30.Exotic Dynamics of Nonholonomic Roller Racer with Periodic Control
Regular and Chaotic Dynamics, 2018, vol. 23, no. 78,pp. 983994
Abstract pdf (1.99 Mb) 
31.An Invariant Measure and the Probability of a Fall in the Problem of an Inhomogeneous Disk Rolling on a Plane
Regular and Chaotic Dynamics, 2018, vol. 23, no. 6,pp. 665684
Abstract pdf (662.06 Kb) 
32.Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability
Regular and Chaotic Dynamics, 2018, vol. 23, no. 5,pp. 613636
Abstract pdf (3.34 Mb) 
33.Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation
Regular and Chaotic Dynamics, 2018, vol. 23, no. 4,pp. 480502
Abstract pdf (2.88 Mb) 
34.A Nonholonomic Model of the Paul Trap
Regular and Chaotic Dynamics, 2018, vol. 23, no. 3,pp. 339354
Abstract pdf (6.87 Mb) 
35.Dynamics of a Body with a Sharp Edge in a Viscous Fluid
Russian Journal of Nonlinear Dynamics, 2018, vol. 14, no. 4,pp. 473494
Abstract pdf (835.37 Kb) 
36.Theoretical and experimental investigations of the rolling of a ball on a rotating plane (turntable)
European Journal of Physics, 2018, vol. 39, no. 6, 065001,13 pp.
Abstract pdf (510.14 Kb) 
37.Dynamics of the Chaplygin ball on a rotating plane
Russian Journal of Mathematical Physics, 2018, vol. 25, no. 4,pp. 423433
Abstract pdf (872.8 Kb)
2017

38.Hamilton’s Principle and the Rolling Motion of a Symmetric Ball
Doklady Physics, 2017, vol. 62, no. 6,pp. 314317
Abstract pdf (206.42 Kb) 
39.Dynamical systems with nonintegrable constraints, vakonomic mechanics, subRiemannian geometry, and nonholonomic mechanics
Russian Mathematical Surveys, 2017, vol. 72, no. 5,pp. 783840
Abstract pdf (1.09 Mb) 
40.Dynamics of Two Point Vortices in an External Compressible Shear Flow
Regular and Chaotic Dynamics, 2017, vol. 22, no. 8,pp. 893–908
Abstract pdf (3.4 Mb) 
41.The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration
Regular and Chaotic Dynamics, 2017, vol. 22, no. 8,pp. 955–975
Abstract pdf (1.91 Mb) 
42.An Inhomogeneous Chaplygin Sleigh
Regular and Chaotic Dynamics, 2017, vol. 22, no. 4,pp. 435447
Abstract pdf (676.55 Kb) 
43.The Hess–Appelrot Case and Quantization of the Rotation Number
Regular and Chaotic Dynamics, 2017, vol. 22, no. 2,pp. 180196
Abstract pdf (991.1 Kb) 
44.An inhomogeneous Chaplygin sleigh
Russian Journal of Nonlinear Dynamics, 2017, vol. 13, no. 4,pp. 625–639
Abstract pdf (518.79 Kb) 
45.The Hess–Appelrot case and quantization of the rotation number
Russian Journal of Nonlinear Dynamics, 2017, vol. 13, no. 3,pp. 433452
Abstract pdf (556.32 Kb) 
46.Integrability and nonintegrability of subRiemannian geodesic flows on Carnot groups
Russian Journal of Nonlinear Dynamics, 2017, vol. 13, no. 1,pp. 129146
Abstract pdf (2.82 Mb) 
47.Optimal control of the motion of a helical body in a liquid using rotors
Russian Journal of Mathematical Physics, 2017, vol. 24, no. 3,pp. 399411
Abstract pdf (582.92 Kb)
2016

48.Generalizations of the Kovalevskaya Case and Quaternions
Proceedings of the Steklov Institute of Mathematics, 2016, vol. 295,pp. 3344
Abstract pdf (190.82 Kb) 
49.The Hess–Appelrot system and its nonholonomic analogs
Proceedings of the Steklov Institute of Mathematics, 2016, vol. 294,pp. 268292
Abstract pdf (1.23 Mb) 
50.Dynamics of a PainlevéAppel system
Journal of Applied Mathematics and Mechanics, 2016, vol. 80, no. 1,pp. 715
Abstract pdf (1.78 Mb) 
51.Describing the Motion of a Body with an Elliptical Cross Section in a Viscous Uncompressible Fluid by Model Equations Reconstructed from Data Processing
Technical Physics Letters, 2016, vol. 42, no. 9,pp. 886890
Abstract pdf (508.12 Kb) 
52.Control of the Motion of a Helical Body in a Fluid Using Rotors
Regular and Chaotic Dynamics, 2016, vol. 21, no. 78,pp. 874884
Abstract pdf (1.23 Mb) 
53.Integrability and Nonintegrability of SubRiemannian Geodesic Flows on Carnot Groups
Regular and Chaotic Dynamics, 2016, vol. 21, no. 6,pp. 759774
Abstract pdf (3.48 Mb) 
54.The Spatial Problem of 2 Bodies on a Sphere. Reduction and Stochasticity
Regular and Chaotic Dynamics, 2016, vol. 21, no. 5,pp. 556580
Abstract pdf (1.45 Mb) 
55.Historical and Critical Review of the Development of Nonholonomic Mechanics: the Classical Period
Regular and Chaotic Dynamics, 2016, vol. 21, no. 4,pp. 455476
Abstract pdf (1.87 Mb) 
56.The Dynamics of Vortex Sources in a Deformation Flow
Regular and Chaotic Dynamics, 2016, vol. 21, no. 3,pp. 367376
Abstract pdf (1.37 Mb) 
57.Adiabatic Invariants, Diffusion and Acceleration in Rigid Body Dynamics
Regular and Chaotic Dynamics, 2016, vol. 21, no. 2,pp. 232248
Abstract pdf (941.28 Kb) 
58.Dynamics of the Chaplygin Sleigh on a Cylinder
Regular and Chaotic Dynamics, 2016, vol. 21, no. 1,pp. 136146
Abstract pdf (268.54 Kb) 
59.Dynamics of the Chaplygin sleigh on a cylinder
Russian Journal of Nonlinear Dynamics, 2016, vol. 12, no. 4,pp. 675–687
Abstract pdf (331.42 Kb) 
60.Historical and critical review of the development of nonholonomic mechanics: the classical period
Russian Journal of Nonlinear Dynamics, 2016, vol. 12, no. 3,pp. 385411
Abstract pdf (1.9 Mb) 
61.On the Hadamard–Hamel problem and the dynamics of wheeled vehicles
Russian Journal of Nonlinear Dynamics, 2016, vol. 12, no. 1,pp. 145163
Abstract pdf (445.79 Kb) 
62.The Hojman Construction and Hamiltonization of Nonholonomic Systems
Symmetry, Integrability and Geometry: Methods and Applications, 2016, vol. 12, 012,19 pp.
Abstract pdf (571.09 Kb) 
63.Rigid Body Dynamics in NonEuclidean Spaces
Russian Journal of Mathematical Physics, 2016, vol. 23, no. 4,pp. 431454
Abstract pdf (704.17 Kb) 
64.Dynamics of a body sliding on a rough plane and supported at three points
Theoretical and Applied Mechanics, 2016, vol. 43, no. 2,pp. 169190
Abstract pdf (1.81 Mb)
2015

65.A New Integrable System of Nonholonomic Mechanics
Doklady Physics, 2015, vol. 60, no. 6,pp. 269271
Abstract pdf (255.48 Kb) 
66.Notes on new friction models and nonholonomic mechanics
PhysicsUspekhi, 2015, vol. 58, no. 12,pp. 12201222
Abstract pdf (262.98 Kb) 
67.Figures of equilibrium of an inhomogeneous selfgravitating fluid
Celestial Mechanics and Dynamical Astronomy, 2015, vol. 122, no. 1,pp. 126
Abstract pdf (651.34 Kb) 
68.On the loss of contact of the Euler disk
Nonlinear Dynamics, 2015, vol. 79, no. 4,pp. 22872294
Abstract pdf (829.12 Kb) 
69.Equations of motion of nonholonomic systems
Russian Mathematical Surveys, 2015, vol. 70, no. 6,pp. 11671169
Abstract pdf (335.26 Kb) 
70.Qualitative Analysis of the Dynamics of a Wheeled Vehicle
Regular and Chaotic Dynamics, 2015, vol. 20, no. 6,pp. 739751
Abstract pdf (445.93 Kb) 
71.On the Hadamard – Hamel Problem and the Dynamics of Wheeled Vehicles
Regular and Chaotic Dynamics, 2015, vol. 20, no. 6,pp. 752766
Abstract pdf (265.93 Kb) 
72.Symmetries and Reduction in Nonholonomic Mechanics
Regular and Chaotic Dynamics, 2015, vol. 20, no. 5,pp. 553604
Abstract pdf (539.38 Kb) 
73.Experimental Investigation of the Motion of a Body with an Axisymmetric Base Sliding on a Rough Plane
Regular and Chaotic Dynamics, 2015, vol. 20, no. 5,pp. 518541
Abstract pdf (516.92 Kb) 
74.The Jacobi Integral in Nonholonomic Mechanics
Regular and Chaotic Dynamics, 2015, vol. 20, no. 3,pp. 383400
Abstract pdf (990.04 Kb) 
75.Dynamics and Control of an Omniwheel Vehicle
Regular and Chaotic Dynamics, 2015, vol. 20, no. 2,pp. 153172
Abstract pdf (1.11 Mb) 
76.Symmetries and Reduction in Nonholonomic Mechanics
Russian Journal of Nonlinear Dynamics, 2015, vol. 11, no. 4,pp. 763–823
Abstract pdf (909.32 Kb) 
77.Topology and Bifurcations in Nonholonomic Mechanics
Russian Journal of Nonlinear Dynamics, 2015, vol. 11, no. 4,pp. 735–762
Abstract pdf (561.73 Kb) 
78.On the dynamics of a body with an axisymmetric base sliding on a rough plane
Russian Journal of Nonlinear Dynamics, 2015, vol. 11, no. 3,pp. 547577
Abstract pdf (2.38 Mb) 
79.The Jacobi Integral in NonholonomicMechanics
Russian Journal of Nonlinear Dynamics, 2015, vol. 11, no. 2,pp. 377396
Abstract pdf (1.9 Mb) 
80.Geometrisation of Chaplygin's reducing multiplier theorem
Nonlinearity, 2015, vol. 28, no. 7,pp. 2307–2318
Abstract pdf (156.41 Kb) 
81.Topology and Bifurcations in Nonholonomic Mechanics
International Journal of Bifurcation and Chaos, 2015, vol. 25, no. 10, 1530028,21 pp.
Abstract pdf (645.53 Kb) 
82.Hamiltonization of Elementary Nonholonomic Systems
Russian Journal of Mathematical Physics, 2015, vol. 22, no. 4,pp. 444453
Abstract pdf (115.49 Kb)
2014

83.On the Nonlinear Poisson Bracket Arising in Nonholonomic Mechanics
Mathematical Notes, 2014, vol. 95, no. 3,pp. 308315
Abstract pdf (509.63 Kb) 
84.Nonholonomic dynamics and Poisson geometry
Russian Mathematical Surveys, 2014, vol. 69, no. 3,pp. 481538
Abstract pdf (917.58 Kb) 
85.On the dynamics of point vortices in an annular region
Fluid Dynamics Research, 2014, vol. 46, no. 3, 031420,7 pp.
Abstract pdf (205.4 Kb) 
86.The Dynamics of Three Vortex Sources
Regular and Chaotic Dynamics, 2014, vol. 19, no. 6,pp. 694701
Abstract pdf (244.27 Kb) 
87.The Dynamics of a Body with an Axisymmetric Base Sliding on a Rough Plane
Regular and Chaotic Dynamics, 2014, vol. 19, no. 6,pp. 607634
Abstract pdf (965.59 Kb) 
88.Superintegrable Generalizations of the Kepler and Hook Problems
Regular and Chaotic Dynamics, 2014, vol. 19, no. 3,pp. 415434
Abstract pdf (300.95 Kb) 
89.The Dynamics of Nonholonomic Systems Consisting of a Spherical Shell with a Moving Rigid Body Inside
Regular and Chaotic Dynamics, 2014, vol. 19, no. 2,pp. 198213
Abstract pdf (241.48 Kb) 
90.The Dynamics of a Rigid Body with a Sharp Edge in Contact with an Inclined Surface in the Presence of Dry Friction
Regular and Chaotic Dynamics, 2014, vol. 19, no. 1,pp. 116139
Abstract pdf (735.75 Kb) 
91.On the dynamics of a body with an axisymmetric base sliding on a rough plane
Russian Journal of Nonlinear Dynamics, 2014, vol. 10, no. 4,pp. 483495
Abstract pdf (667.35 Kb) 
92.Invariant Measure and Hamiltonization of Nonholonomic Systems
Russian Journal of Nonlinear Dynamics, 2014, vol. 10, no. 3,pp. 355359
Abstract pdf (283.75 Kb) 
93.The dynamics of three vortex sources
Russian Journal of Nonlinear Dynamics, 2014, vol. 10, no. 3,pp. 319327
Abstract pdf (413.32 Kb) 
94.Figures of equilibrium of an inhomogeneous selfgravitating fluid
Russian Journal of Nonlinear Dynamics, 2014, vol. 10, no. 1,pp. 73100
Abstract pdf (492.78 Kb) 
95.The dynamics of vortex rings: leapfrogging in an ideal and viscous fluid
Fluid Dynamics Research, 2014, vol. 46, no. 3, 031415,16 pp.
Abstract pdf (746.69 Kb)
2013

96.The Problem of Drift and Recurrence for the Rolling Chaplygin Ball
Regular and Chaotic Dynamics, 2013, vol. 18, no. 6,pp. 832859
Abstract pdf (702.93 Kb) 
97.The Dynamics of the Chaplygin Ball with a Fluidfilled Cavity
Regular and Chaotic Dynamics, 2013, vol. 18, no. 5,pp. 490496
Abstract pdf (405.38 Kb) 
98.Topological Analysis of an Integrable System Related to the Rolling of a Ball on a Sphere
Regular and Chaotic Dynamics, 2013, vol. 18, no. 4,pp. 356371
Abstract pdf (488.37 Kb) 
99.The Hierarchy of Dynamics of a Rigid Body Rolling without Slipping and Spinning on a Plane and a Sphere
Regular and Chaotic Dynamics, 2013, vol. 18, no. 3,pp. 277328
Abstract pdf (2.69 Mb) 
100.How to Control the Chaplygin Ball Using Rotors. II
Regular and Chaotic Dynamics, 2013, vol. 18, no. 12,pp. 144158
Abstract pdf (1.73 Mb) 
101.The Selfpropulsion of a Body with Moving Internal Masses in a Viscous Fluid
Regular and Chaotic Dynamics, 2013, vol. 18, no. 12,pp. 100117
Abstract pdf (1.71 Mb) 
102.The Dynamics of Vortex Rings: Leapfrogging, Choreographies and the Stability Problem
Regular and Chaotic Dynamics, 2013, vol. 18, no. 12,pp. 3362
Abstract pdf (857.35 Kb) 
103.The problem of drift and recurrence for the rolling Chaplygin ball
Russian Journal of Nonlinear Dynamics, 2013, vol. 9, no. 4,pp. 721754
Abstract pdf (875.6 Kb) 
104.Geometrization of the Chaplygin reducingmultiplier theorem
Russian Journal of Nonlinear Dynamics, 2013, vol. 9, no. 4,pp. 627640
Abstract pdf (373.67 Kb) 
105.The dynamics of rigid body whose sharp edge is in contact with a inclined surface with dry friction
Russian Journal of Nonlinear Dynamics, 2013, vol. 9, no. 3,pp. 567594
Abstract pdf (886.59 Kb) 
106.The dynamics of nonholonomic systems consisting of a spherical shell with a moving rigid body inside
Russian Journal of Nonlinear Dynamics, 2013, vol. 9, no. 3,pp. 547566
Abstract pdf (441.83 Kb) 
107.On the dynamics of a body with an axisymmetric base sliding on a rough plane
Russian Journal of Nonlinear Dynamics, 2013, vol. 9, no. 3,pp. 521545
Abstract pdf (612.94 Kb) 
108.On the loss of contact of the Euler disk
Russian Journal of Nonlinear Dynamics, 2013, vol. 9, no. 3,pp. 499506
Abstract pdf (362.06 Kb) 
109.The hierarchy of dynamics of a rigid body rolling without slipping and spinning on a plane and a sphere
Russian Journal of Nonlinear Dynamics, 2013, vol. 9, no. 2,pp. 141202
Abstract pdf (7.91 Mb) 
110.How to control the Chaplygin ball using rotors. II
Russian Journal of Nonlinear Dynamics, 2013, vol. 9, no. 1,pp. 5976
Abstract pdf (2.71 Mb) 
111.Rolling of a Rigid Body Without Slipping and Spinning: Kinematics and Dynamics
Journal of Applied Nonlinear Dynamics, 2013, vol. 2, no. 2,pp. 161173
Abstract pdf (269.77 Kb)
2012

112.Rolling of a Ball without Spinning on a Plane: the Absence of an Invariant Measure in a System with a Complete Set of Integrals
Regular and Chaotic Dynamics, 2012, vol. 17, no. 6,pp. 571579
Abstract pdf (402.12 Kb) 
113.The Bifurcation Analysis and the Conley Index in Mechanics
Regular and Chaotic Dynamics, 2012, vol. 17, no. 5,pp. 457478
Abstract pdf (614.32 Kb) 
114.How to Control Chaplygin’s Sphere Using Rotors
Regular and Chaotic Dynamics, 2012, vol. 17, no. 34,pp. 258272
Abstract pdf (242.89 Kb) 
115.Two Nonholonomic Integrable Problems Tracing Back to Chaplygin
Regular and Chaotic Dynamics, 2012, vol. 17, no. 2,pp. 191198
Abstract pdf (150.32 Kb) 
116.Generalized Chaplygin’s Transformation and Explicit Integration of a System with a Spherical Support
Regular and Chaotic Dynamics, 2012, vol. 17, no. 2,pp. 170190
Abstract pdf (484.82 Kb) 
117.Topological analysis of one integrable system related to the rolling of a ball over a sphere
Russian Journal of Nonlinear Dynamics, 2012, vol. 8, no. 5,pp. 957975
Abstract pdf (796.84 Kb) 
118.The motion of a body with variable mass geometry in a viscous fluid
Russian Journal of Nonlinear Dynamics, 2012, vol. 8, no. 4,pp. 815836
Abstract pdf (15.9 Mb) 
119.Rolling of a rigid body without slipping and spinning: kinematics and dynamics
Russian Journal of Nonlinear Dynamics, 2012, vol. 8, no. 4,pp. 783797
Abstract pdf (347.06 Kb) 
120.Rolling without spinning of a ball on a plane: absence of an invariant measure in a system with a complete set of first integrals
Russian Journal of Nonlinear Dynamics, 2012, vol. 8, no. 3,pp. 605616
Abstract pdf (328.96 Kb) 
121.How to control the Chaplygin sphere using rotors
Russian Journal of Nonlinear Dynamics, 2012, vol. 8, no. 2,pp. 289307
Abstract pdf (400.44 Kb) 
122.The dynamics of vortex rings: Leapfrogging, choreographies and the stability problem
Russian Journal of Nonlinear Dynamics, 2012, vol. 8, no. 1,pp. 113147
Abstract pdf (1.03 Mb) 
123.The dynamics of the Chaplygin ball with a fluidfilled cavity
Russian Journal of Nonlinear Dynamics, 2012, vol. 8, no. 1,pp. 103111
Abstract pdf (305.43 Kb)
2011

124.On the Model of Nonholonomic Billiard
Regular and Chaotic Dynamics, 2011, vol. 16, no. 6,pp. 653662
Abstract pdf (199.9 Kb) 
125.Rolling of a Homogeneous Ball over a Dynamically Asymmetric Sphere
Regular and Chaotic Dynamics, 2011, vol. 16, no. 5,pp. 465483
Abstract pdf (643.15 Kb) 
126.Hamiltonization of Nonholonomic Systems in the Neighborhood of Invariant Manifolds
Regular and Chaotic Dynamics, 2011, vol. 16, no. 5,pp. 443464
Abstract pdf (425.83 Kb) 
127.Hamiltonicity and integrability of the Suslov problem
Regular and Chaotic Dynamics, 2011, vol. 16, no. 12,pp. 104116
Abstract pdf (239.81 Kb) 
128.An omniwheel vehicle on a plane and a sphere
Russian Journal of Nonlinear Dynamics, 2011, vol. 7, no. 4,pp. 785801
Abstract pdf (726.7 Kb) 
129.The bifurcation analysis and the Conley index in mechanics
Russian Journal of Nonlinear Dynamics, 2011, vol. 7, no. 3,pp. 649681
Abstract pdf (782.35 Kb) 
130.Two nonholonomic integrable systems of coupled rigid bodies
Russian Journal of Nonlinear Dynamics, 2011, vol. 7, no. 3,pp. 559568
Abstract pdf (404.52 Kb) 
131.On V.A. Steklov’s legacy in classical mechanics
Russian Journal of Nonlinear Dynamics, 2011, vol. 7, no. 2,pp. 389403
Abstract pdf (368.21 Kb) 
132.Generalized Chaplygin’s transformation and explicit integration of a system with a spherical support
Russian Journal of Nonlinear Dynamics, 2011, vol. 7, no. 2,pp. 313338
Abstract pdf (1.78 Mb) 
133.Stability of new relative equilibria of the system of three point vortices in a circular domain
Russian Journal of Nonlinear Dynamics, 2011, vol. 7, no. 1,pp. 119138
Abstract pdf (1.2 Mb)
2010

134.Basic principles and models of dynamic advection
Doklady Physics, 2010, vol. 432, no. 1,pp. 41–44
Abstract pdf (178.99 Kb) 
135.Topology and stability of integrable systems
Russian Mathematical Surveys, 2010, vol. 65, no. 2,pp. 259–318
Abstract pdf (1.12 Mb) 
136.Coupled motion of a rigid body and point vortices on a twodimensional spherical surface
Regular and Chaotic Dynamics, 2010, vol. 15, no. 45,pp. 440461
Abstract pdf (298.75 Kb) 
137.Reply to A. T. Fomenko's comments
Russian Journal of Nonlinear Dynamics, 2010, vol. 6, no. 4,pp. 893895
Abstract pdf (97.18 Kb) 
138.Rolling of a homogeneous ball over a dynamically asymmetric sphere
Russian Journal of Nonlinear Dynamics, 2010, vol. 6, no. 4,pp. 869889
Abstract pdf (486.45 Kb) 
139.Hamiltonisation of nonholonomic systems in the neighborhood of invariant manifolds
Russian Journal of Nonlinear Dynamics, 2010, vol. 6, no. 4,pp. 829854
Abstract pdf (398.78 Kb) 
140.Stability of a liquid selfgravitating elliptic cylinder with intrinsic rotation
Russian Journal of Nonlinear Dynamics, 2010, vol. 6, no. 4,pp. 807822
Abstract pdf (902.16 Kb) 
141.Dynamic advection
Russian Journal of Nonlinear Dynamics, 2010, vol. 6, no. 3,pp. 521530
Abstract pdf (10.3 Mb) 
142.Valery Vasilievich Kozlov. On his 60th birthday
Russian Journal of Nonlinear Dynamics, 2010, vol. 6, no. 3,pp. 461488
Abstract pdf (25.39 Mb) 
143.On the model of nonholonomic billiard
Russian Journal of Nonlinear Dynamics, 2010, vol. 6, no. 2,pp. 373385
Abstract pdf (237.96 Kb) 
144.Problems of stability and asymptotic behavior of vortex patches on the plane
Russian Journal of Nonlinear Dynamics, 2010, vol. 6, no. 2,pp. 327343
Abstract pdf (685.19 Kb) 
145.Hamiltonian representation and integrability of the Suslov problem
Russian Journal of Nonlinear Dynamics, 2010, vol. 6, no. 1,pp. 127142
Abstract pdf (654.76 Kb) 
146.Dynamics of a wheeled carriage on a plane
Bulletin of Udmurt University. Mathematics. Mechanics. Computer Science, 2010, no. 4,pp. 3948
Abstract pdf (385.82 Kb) 
147.Lyapunov A.M. Works on theoretical mechanics. From the 18821894 handwritten heritage
Izhevsk: Regular and Chaotic Dynamics, 2010,pp. 620
Abstract pdf (174.49 Kb)
2009

148.The dynamics of a Chaplygin sleigh
Journal of Applied Mathematics and Mechanics, 2009, vol. 73, no. 2,pp. 156161
Abstract pdf (263.77 Kb) 
149.Superintegrable system on a sphere with the integral of higher degree
Regular and Chaotic Dynamics, 2009, vol. 14, no. 6,pp. 615620
Abstract pdf (125.27 Kb) 
150.Isomorphisms of geodesic flows on quadrics
Regular and Chaotic Dynamics, 2009, vol. 14, no. 45,pp. 455465
Abstract pdf (376.58 Kb) 
151.The Hamiltonian Dynamics of Selfgravitating Liquid and Gas Ellipsoids
Regular and Chaotic Dynamics, 2009, vol. 14, no. 2,pp. 179217
Abstract pdf (885.59 Kb) 
152.Multiparticle Systems. The Algebra of Integrals and Integrable Cases
Regular and Chaotic Dynamics, 2009, vol. 14, no. 1,pp. 1841
Abstract pdf (472.45 Kb) 
153.New superintegrable system on a sphere
Russian Journal of Nonlinear Dynamics, 2009, vol. 5, no. 4,pp. 455462
Abstract pdf (214.58 Kb) 
154.Statistical mechanics of nonlinear dynamical systems
Russian Journal of Nonlinear Dynamics, 2009, vol. 5, no. 3,pp. 385402
Abstract pdf (896.55 Kb) 
155.Coupled motion of a rigid body and point vortices on a sphere
Russian Journal of Nonlinear Dynamics, 2009, vol. 5, no. 3,pp. 319343
Abstract pdf (429.33 Kb) 
156.Isomorphisms of geodesic flows on quadrics
Russian Journal of Nonlinear Dynamics, 2009, vol. 5, no. 2,pp. 145158
Abstract pdf (532.83 Kb) 
157.Multiparticle Systems. The Algebra of Integrals and Integrable Cases
Russian Journal of Nonlinear Dynamics, 2009, vol. 5, no. 1,pp. 5382
Abstract pdf (508.81 Kb)
2008

158.Explicit integration of one problem in nonholonomic mechanics
Doklady Physics, 2008, vol. 53, no. 10,pp. 525528
Abstract pdf (229.05 Kb) 
159.Chaplygin ball over a fixed sphere: an explicit integration
Regular and Chaotic Dynamics, 2008, vol. 13, no. 6,pp. 557571
Abstract pdf (282.96 Kb) 
160.Conservation Laws, Hierarchy of Dynamics and Explicit Integration of Nonholonomic Systems
Regular and Chaotic Dynamics, 2008, vol. 13, no. 5,pp. 443490
Abstract pdf (508.23 Kb) 
161.Stability of Steady Rotations in the Nonholonomic Routh Problem
Regular and Chaotic Dynamics, 2008, vol. 13, no. 4,pp. 239249
Abstract pdf (392.42 Kb) 
162.Chaos in a Restricted Problem of Rotation of a Rigid Body with a Fixed Point
Regular and Chaotic Dynamics, 2008, vol. 13, no. 3,pp. 221233
Abstract pdf (491.62 Kb) 
163.Absolute and Relative Choreographies in Rigid Body Dynamics
Regular and Chaotic Dynamics, 2008, vol. 13, no. 3,pp. 204220
Abstract pdf (447.19 Kb) 
164.Algebraic reduction of systems on two and threedimensional spheres
Russian Journal of Nonlinear Dynamics, 2008, vol. 4, no. 4,pp. 407416
Abstract pdf (180.6 Kb) 
165.Hamiltonian Dynamics of Liquid and Gas SelfGravitating Ellipsoids
Russian Journal of Nonlinear Dynamics, 2008, vol. 4, no. 4,pp. 363406
Abstract pdf (994.54 Kb) 
166.Conservation Laws, Hierarchy of Dynamics and Explicit Integration of Nonholonomic Systems
Russian Journal of Nonlinear Dynamics, 2008, vol. 4, no. 3,pp. 223280
Abstract pdf (634.39 Kb) 
167.Dynamics of Two Rings of Vortices on a Sphere
in IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence, Springer, 2008, vol. 6,pp. 445–458
Abstract pdf (7.9 Mb) 
168.A New Integrable Problem of Motion of Point Vortices on the Sphere
in IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence, Springer, 2008, vol. 6,pp. 39–53
Abstract pdf (10.34 Mb)
2007

169.Isomorphism and Hamilton representation of some nonholonomic systems
Siberian Mathematical Journal, 2007, vol. 48, no. 1,pp. 2636
Abstract pdf (154.1 Kb) 
170.Asymptotic stability and associated problems of dynamics of falling rigid body
Regular and Chaotic Dynamics, 2007, vol. 12, no. 5,pp. 531565
Abstract pdf (1.81 Mb) 
171.Rolling of a Nonhomogeneous Ball Over a Sphere Without Slipping and Twisting
Regular and Chaotic Dynamics, 2007, vol. 12, no. 2,pp. 153159
Abstract pdf (189.47 Kb) 
172.Interaction between Kirchhoff vortices and point vortices in an ideal fluid
Regular and Chaotic Dynamics, 2007, vol. 12, no. 1,pp. 6880
Abstract pdf (358.32 Kb) 
173.Motion of two spheres in ideal fluid. I. Equations o motions in the Euclidean space. First integrals and reduction
Russian Journal of Nonlinear Dynamics, 2007, vol. 3, no. 4,pp. 411422
Abstract pdf (182.63 Kb) 
174.Asymptotic stability and associated problems of dynamics of falling rigid body
Russian Journal of Nonlinear Dynamics, 2007, vol. 3, no. 3,pp. 255296
Abstract pdf (1.62 Mb) 
175.A New Integrable Problem of Motion of Point Vortices on the Sphere
Russian Journal of Nonlinear Dynamics, 2007, vol. 3, no. 2,pp. 211223
Abstract pdf (298.41 Kb) 
176.On isomorphisms of some integrable systems on a plane and a sphere
Russian Journal of Nonlinear Dynamics, 2007, vol. 3, no. 1,pp. 4956
Abstract pdf (166.52 Kb) 
177.Dynamic Interaction of Point Vortices and a TwoDimensional Cylinder
Journal of Mathematical Physics, 2007, vol. 48, no. 6, 065403,9 pp.
Abstract pdf (126.99 Kb) 
178.Relations between Integrable Systems in Plane and Curved Spaces
Celestial Mechanics and Dynamical Astronomy, 2007, vol. 99, no. 4,pp. 253–260
Abstract pdf (151.07 Kb) 
179.Dynamics of Two Interacting Circular Cylinders in Perfect Fluid
Discrete and Continuous Dynamical Systems  Series A, 2007, vol. 19, no. 2,pp. 235253
Abstract pdf (350.69 Kb)
2006

180.New effects in dynamics of rattlebacks
Doklady Physics, 2006, vol. 408, no. 2,pp. 192195
Abstract pdf (214.19 Kb) 
181.Transition to chaos in dynamics of four point vortices on a plane
Doklady Physics, 2006, vol. 51, no. 5,pp. 262267
Abstract pdf (249.72 Kb) 
182.Motion of Chaplygin ball on an inclined plane
Doklady Physics, 2006, vol. 51, no. 2,pp. 7376
Abstract pdf (212.42 Kb) 
183.An Integrable System with a Nonintegrable Constraint
Mathematical Notes, 2006, vol. 80, no. 1,pp. 127130
Abstract pdf (98.56 Kb) 
184.On a Nonholonomic Dynamical Problem
Mathematical Notes, 2006, vol. 79, no. 5,pp. 734740
Abstract pdf (189.22 Kb) 
185.On the problem of motion of vortex sources on a plane
Regular and Chaotic Dynamics, 2006, vol. 11, no. 4,pp. 455466
Abstract pdf (377.53 Kb) 
186.Rolling of a heterotgeneous ball over a sphere without sliding and spinning
Russian Journal of Nonlinear Dynamics, 2006, vol. 2, no. 4,pp. 445452
Abstract pdf (162.92 Kb) 
187.Stability of steady rotations in the nonholonomic Routh problem
Russian Journal of Nonlinear Dynamics, 2006, vol. 2, no. 3,pp. 333345
Abstract pdf (398.23 Kb) 
188.Reduction in the twobody problem on the Lobatchevsky plane
Russian Journal of Nonlinear Dynamics, 2006, vol. 2, no. 3,pp. 279285
Abstract pdf (148.66 Kb) 
189.Interaction between Kirchhoff vortices and point vortices in an ideal fluid
Russian Journal of Nonlinear Dynamics, 2006, vol. 2, no. 2,pp. 199213
Abstract pdf (535.61 Kb) 
190.Dynamics of two vortex rings on a sphere
Russian Journal of Nonlinear Dynamics, 2006, vol. 2, no. 2,pp. 181192
Abstract pdf (321.21 Kb) 
191.On the motion of a heavy rigid body in an ideal fluid with circulation
Chaos, 2006, vol. 16, no. 1, 013118,7 pp.
Abstract pdf (303.93 Kb) 
192.The restricted twobody problem in constant curvature spaces
Celestial Mechanics and Dynamical Astronomy, 2006, vol. 96, no. 1,pp. 117
Abstract pdf (479.18 Kb) 
193.Classification of BirkhoffIntegrable generalized Toda lattices
in "Topological Methods in the Theory of Integrable Systems", Cambridge: Cambridge Scientific Publishers Ltd., 2006,pp. 6979
Abstract pdf (560.25 Kb)
2005

194.Absolute and Relative Choreographies in the Problem of the Motion of Point Vortices in a Plane
Doklady Physics, 2005, vol. 71, no. 1,pp. 139144
Abstract pdf (168.54 Kb) 
195.The Nonexistence of an Invariant Measure for an Inhomogeneous Ellipsoid Rolling on a Plane
Mathematical Notes, 2005, vol. 77, no. 6,pp. 855857
Abstract pdf (74.38 Kb) 
196.Superintegrable systems on a sphere
Regular and Chaotic Dynamics, 2005, vol. 10, no. 3,pp. 257266
Abstract pdf (312.81 Kb) 
197.Reduction and chaotic behavior of point vortices on a plane and a sphere
Russian Journal of Nonlinear Dynamics, 2005, vol. 1, no. 2,pp. 233246
Abstract pdf (473.55 Kb) 
198.Chaos in a restricted problem of rotation of a rigid body with a fixed point
Russian Journal of Nonlinear Dynamics, 2005, vol. 1, no. 2,pp. 191207
Abstract pdf (650.7 Kb) 
199.Absolute and relative choreographies in rigid body dynamics
Russian Journal of Nonlinear Dynamics, 2005, vol. 1, no. 1,pp. 123141
Abstract pdf (401.63 Kb) 
200.Interaction of two circular cylinders in a perfect fluid
Russian Journal of Nonlinear Dynamics, 2005, vol. 1, no. 1,pp. 321
Abstract pdf (401.14 Kb) 
201.Dynamics of a circular cylinder interacting with point vortices
Discrete and Continuous Dynamical Systems  Series B, 2005, vol. 5, no. 1,pp. 3550
Abstract pdf (210.01 Kb) 
202.Generalized problem of two and four Newtonian centers
Celestial Mechanics and Dynamical Astronomy, 2005, vol. 92, no. 4,pp. 371380
Abstract pdf (291.25 Kb) 
203.Reduction and chaotic behavior of point vortices on a plane and a sphere
Discrete and Continuous Dynamical Systems  Series B (Supplement Volume devoted to the 5th AIMS International Conference on Dynamical Systems and Differential Equations (Pomona, California, USA, June 2004)), 2005,pp. 100109
Abstract pdf (360.5 Kb) 
204.New periodic solutions for three or four identical vortices on a plane and a sphere
Discrete and Continuous Dynamical Systems  Series B (Supplement Volume devoted to the 5th AIMS International Conference on Dynamical Systems and Differential Equations (Pomona, California, USA, June 2004)), 2005,pp. 110120
Abstract pdf (194.7 Kb)
2004

205.Necessary and Sufficient Conditions for the Polynomial Integrability of Generalized Toda Chains
Doklady Physics, 2004, vol. 69, no. 1,pp. 131135
Abstract pdf (280.72 Kb) 
206.Integrability of the Problem of the Motion of a Cylinder and a Vortex in an Ideal Fluid
Mathematical Notes, 2004, vol. 75, no. 1,pp. 1922
Abstract pdf (79.87 Kb) 
207.Twobody problem on a sphere. Reduction, stochasticity, periodic orbits
Regular and Chaotic Dynamics, 2004, vol. 9, no. 3,pp. 265279
Abstract pdf (13.58 Mb) 
208.Absolute and relative choreographies in the problem of point vortices moving on a plane
Regular and Chaotic Dynamics, 2004, vol. 9, no. 2,pp. 101111
Abstract pdf (389.11 Kb)
2003

209.Two Integrable System on a Twodimensional Sphere
Doklady Physics, 2003, vol. 389, no. 3,pp. 338340
Abstract pdf (160.12 Kb) 
210.Strange Attractors in Rattleback Dynamics
PhysicsUspekhi, 2003, vol. 46, no. 4,pp. 393403
Abstract pdf (484.78 Kb) 
211.The Hess case in the dynamics of a rigid body
Journal of Applied Mathematics and Mechanics, 2003, vol. 67, no. 2,pp. 227235
Abstract pdf (605.38 Kb) 
212.Motion of a circular cylinder and $n$ point vortices in a perfect fluid
Regular and Chaotic Dynamics, 2003, vol. 8, no. 4,pp. 449462
Abstract pdf (585.43 Kb) 
213.New cases when the invariant measure and first integrals exist in the problem of a body rolling on a surface
Regular and Chaotic Dynamics, 2003, vol. 8, no. 3,pp. 331335
Abstract pdf (148.37 Kb) 
214.Dynamics of rolling disk
Regular and Chaotic Dynamics, 2003, vol. 8, no. 2,pp. 201212
Abstract pdf (648.4 Kb) 
215.An Integrability of the Problem on Motion of Cylinder and Vortex in the Ideal Fluid
Regular and Chaotic Dynamics, 2003, vol. 8, no. 2,pp. 163166
Abstract pdf (90.36 Kb)
2002

216.Obstacle to the Reduction of Nonholonomic Systems to the Hamiltonian Form
Doklady Physics, 2002, vol. 47, no. 12,pp. 892894
Abstract pdf (36.81 Kb) 
217.A New Integral in the Problem of Rolling a Ball on an Arbitrary Ellipsoid
Doklady Physics, 2002, vol. 47, no. 7,pp. 544547
Abstract pdf (85.97 Kb) 
218.The rolling motion of a ball on a surface. New integrals and hierarchy of dynamics
Regular and Chaotic Dynamics, 2002, vol. 7, no. 2,pp. 201219
Abstract pdf (628.29 Kb) 
219.The rolling motion of a rigid body on a plane and a sphere. Hierarchy of dynamics
Regular and Chaotic Dynamics, 2002, vol. 7, no. 2,pp. 177200
Abstract pdf (784.15 Kb) 
220.On the History of the Development of the Nonholonomic Dynamics
Regular and Chaotic Dynamics, 2002, vol. 7, no. 1,pp. 4347
Abstract pdf (183.63 Kb) 
221.Generalization of the Goryachev–Chaplygin Case
Regular and Chaotic Dynamics, 2002, vol. 7, no. 1,pp. 2130
Abstract pdf (289.22 Kb)
2001

222.A New Integrable Case on $so(4)$
Doklady Physics, 2001, vol. 46, no. 12,pp. 888889
Abstract pdf (28.12 Kb) 
223.Chaplygin's Ball Rolling Problem Is Hamiltonian
Mathematical Notes, 2001, vol. 70, no. 5,pp. 720723
Abstract pdf (339.65 Kb) 
224.Euler–Poisson Equations and Integrable Cases
Regular and Chaotic Dynamics, 2001, vol. 6, no. 3,pp. 253276
Abstract pdf (1.41 Mb) 
225.Kovalevskaya top and generalizations of integrable systems
Regular and Chaotic Dynamics, 2001, vol. 6, no. 1,pp. 116
Abstract pdf (286.68 Kb)
2000

226.Some comments to the paper by A.M.Perelomov "A note on geodesics on ellipsoid" RCD 2000 5(1) 8991
Regular and Chaotic Dynamics, 2000, vol. 5, no. 1,pp. 9294
Abstract pdf (178.43 Kb) 
227.The Kovalevskaya case and new integrable systems of dynamics
Vestnik molodyh uchenyh. "Prikladnaya matematika i mehanika", 2000, no. 4,pp. 1325
Abstract pdf (910.69 Kb)
1999

228.The restricted twobody problem and the kepler problem in the constant curvature spaces
Regular and Chaotic Dynamics, 1999, vol. 4, no. 2,pp. 112124
Abstract pdf (807.85 Kb) 
229.Lie algebras in vortex dynamics and celestial mechanics — IV
Regular and Chaotic Dynamics, 1999, vol. 4, no. 1,pp. 2350
Abstract pdf (1.16 Mb)
1998

230.Libration points in a bounded problem of three bodies on $S^2$
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 1998, no. 1,pp. 6166
Abstract pdf (3.96 Mb) 
231.Integrability of the Problems of Motion of a Particle in Constant Curvature Spaces in the Presence of Magnetic Monopole and in the Presence of Two Fixed Newtonian Centers
Proceedings of IX Seminar "Gravitational Energy and Gravity Waves", 1998,pp. 7578
Abstract pdf (4.6 Mb) 
232.A degenerate Poisson Structure and Lie algebras in the Two Problems of Hamiltonian Dynamics
Proceedings of IX Seminar "Gravitational Energy and Gravity Waves", 1998,pp. 7174
Abstract pdf (3.81 Mb)
1997

233.Nonlinear Poisson brackets and isomorphisms in dynamics
Regular and Chaotic Dynamics, 1997, vol. 2, no. 34,pp. 7289
Abstract pdf (1.69 Mb) 
234.Adiabatic Chaos in Rigid Body Dynamics
Regular and Chaotic Dynamics, 1997, vol. 2, no. 2,pp. 6578
Abstract pdf (1.71 Mb)