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2022

  • 1.

    Bizyaev I. A., Mamaev I. S.

    Bifurcation diagram and a qualitative analysis of particle motion in a Kerr metric
    Physical Review D, 2022, vol. 105, 063003, 28 pp.
    Abstract          pdf  (2.68 Mb)

2021

  • 2.

    Bizyaev I. A., Mamaev I. S.

    Qualitative Analysis of the Dynamics of a Balanced Circular Foil and a Vortex
    Regular and Chaotic Dynamics, 2021, vol. 26, no. 6, pp. 658-674
    Abstract          pdf  (1.34 Mb)
  • 3.

    Bizyaev I. A., Bolotin S. V., Mamaev I. S.

    Normal forms and averaging in an acceleration problem in nonholonomic mechanics
    Chaos, 2021, vol. 31, 013132, 16 pp.
    Abstract          pdf  (1.05 Mb)
  • 4.

    Mamaev I. S., Bizyaev I. A.

    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.

    Bizyaev I. A., Mamaev I. S.

    Separatrix splitting and nonintegrability in the nonholonomic rolling of a generalized Chaplygin sphere
    International Journal of Non-Linear Mechanics, 2020, vol. 126, 103550, 7 pp.
    Abstract          pdf  (2.22 Mb)
  • 6.

    Bizyaev I. A., Mamaev I. S.

    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. 618-627
    Abstract          pdf  (553.19 Kb)
  • 7.

    Bizyaev I. A., Mamaev I. S.

    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)
  • 8.

    Mamaev I. S., Bizyaev I. A.

    Dynamics of point vortices and a cylinder in an ideal fluid
    2020 International Conference Nonlinearity, Information and Robotics – IEEE, 2020, pp. 1-3
    Abstract          pdf  (241.98 Kb)

2019

  • 9.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    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. 560-582
    Abstract          pdf  (1.93 Mb)
  • 10.

    Bizyaev I. A., Borisov A. V., Kuznetsov S. P.

    The Chaplygin sleigh with friction moving due to periodic oscillations of an internal mass
    Nonlinear Dynamics, 2019, vol. 95, no. 1, pp. 699-714
    Abstract          pdf  (2.97 Mb)
  • 11.

    Bizyaev I. A., Borisov A. V., Kozlov V. V., Mamaev I. S.

    Fermi-like acceleration and power-law energy growth in nonholonomic systems
    Nonlinearity, 2019, vol. 32, pp. 3209-3233
    Abstract          pdf  (974.09 Kb)
  • 12.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    Dynamics of a Chaplygin sleigh with an unbalanced rotor: regular and chaotic motions
    Nonlinear Dynamics, 2019, vol. 98, pp. 2277-2291
    Abstract          pdf  (829 Kb)

2018

  • 13.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    Exotic Dynamics of Nonholonomic Roller Racer with Periodic Control
    Regular and Chaotic Dynamics, 2018, vol. 23, no. 7-8, pp. 983-994
    Abstract          pdf  (1.99 Mb)
  • 14.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    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. 665-684
    Abstract          pdf  (662.06 Kb)
  • 15.

    Borisov A. V., Mamaev I. S., Bizyaev I. A.

    Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability
    Regular and Chaotic Dynamics, 2018, vol. 23, no. 5, pp. 613-636
    Abstract          pdf  (3.34 Mb)
  • 16.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    Dynamics of the Chaplygin ball on a rotating plane
    Russian Journal of Mathematical Physics, 2018, vol. 25, no. 4, pp. 423-433
    Abstract          pdf  (872.8 Kb)

2017

  • 17.

    Borisov A. V., Mamaev I. S., Bizyaev I. A.

    Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics
    Russian Mathematical Surveys, 2017, vol. 72, no. 5, pp. 783-840
    Abstract          pdf  (1.09 Mb)
  • 18.

    Bizyaev I. A.

    A Chaplygin sleigh with a moving point mass
    Bulletin of Udmurt University. Mathematics. Mechanics. Computer Science, 2017, vol. 27, no. 4, pp. 583-589
    Abstract          pdf  (314.6 Kb)
  • 19.

    Bizyaev I. A.

    Invariant measure in the problem of a disk rolling on a plane
    Bulletin of Udmurt University. Mathematics. Mechanics. Computer Science, 2017, vol. 27, no. 4, pp. 576-582
    Abstract          pdf  (312.38 Kb)
  • 20.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    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)
  • 21.

    Bizyaev I. A.

    The Inertial Motion of a Roller Racer
    Regular and Chaotic Dynamics, 2017, vol. 22, no. 3, pp. 239-247
    Abstract          pdf  (3.26 Mb)
  • 22.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    The Hess–Appelrot Case and Quantization of the Rotation Number
    Regular and Chaotic Dynamics, 2017, vol. 22, no. 2, pp. 180-196
    Abstract          pdf  (991.1 Kb)
  • 23.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    The Hess–Appelrot case and quantization of the rotation number
    Russian Journal of Nonlinear Dynamics, 2017, vol. 13, no. 3, pp. 433-452
    Abstract          pdf  (556.32 Kb)
  • 24.

    Bizyaev I. A., Borisov A. V., Kilin A. A., Mamaev I. S.

    Integrability and nonintegrability of sub-Riemannian geodesic flows on Carnot groups
    Russian Journal of Nonlinear Dynamics, 2017, vol. 13, no. 1, pp. 129-146
    Abstract          pdf  (2.82 Mb)
  • 25.

    Bizyaev I. A., Borisov A. V., Kuznetsov S. P.

    Chaplygin sleigh with periodically oscillating internal mass
    EPL, 2017, vol. 119, no. 6, 60008, 7 pp.
    Abstract          pdf  (854.88 Kb)

2016

  • 26.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    Generalizations of the Kovalevskaya Case and Quaternions
    Proceedings of the Steklov Institute of Mathematics, 2016, vol. 295, pp. 33-44
    Abstract          pdf  (190.82 Kb)
  • 27.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    The Hess–Appelrot system and its nonholonomic analogs
    Proceedings of the Steklov Institute of Mathematics, 2016, vol. 294, pp. 268-292
    Abstract          pdf  (1.23 Mb)
  • 28.

    Bizyaev I. A., Borisov A. V., Kilin A. A., Mamaev I. S.

    Integrability and Nonintegrability of Sub-Riemannian Geodesic Flows on Carnot Groups
    Regular and Chaotic Dynamics, 2016, vol. 21, no. 6, pp. 759-774
    Abstract          pdf  (3.48 Mb)
  • 29.

    Borisov A. V., Mamaev I. S., Bizyaev I. A.

    The Spatial Problem of 2 Bodies on a Sphere. Reduction and Stochasticity
    Regular and Chaotic Dynamics, 2016, vol. 21, no. 5, pp. 556-580
    Abstract          pdf  (1.45 Mb)
  • 30.

    Borisov A. V., Mamaev I. S., Bizyaev I. A.

    Historical and Critical Review of the Development of Nonholonomic Mechanics: the Classical Period
    Regular and Chaotic Dynamics, 2016, vol. 21, no. 4, pp. 455-476
    Abstract          pdf  (1.87 Mb)
  • 31.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    The Dynamics of Vortex Sources in a Deformation Flow
    Regular and Chaotic Dynamics, 2016, vol. 21, no. 3, pp. 367-376
    Abstract          pdf  (1.37 Mb)
  • 32.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    Dynamics of the Chaplygin Sleigh on a Cylinder
    Regular and Chaotic Dynamics, 2016, vol. 21, no. 1, pp. 136-146
    Abstract          pdf  (268.54 Kb)
  • 33.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    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)
  • 34.

    Borisov A. V., Mamaev I. S., Bizyaev I. A.

    Historical and critical review of the development of nonholonomic mechanics: the classical period
    Russian Journal of Nonlinear Dynamics, 2016, vol. 12, no. 3, pp. 385-411
    Abstract          pdf  (1.9 Mb)
  • 35.

    Bizyaev I. A., Borisov A. V., Kazakov A. O.

    Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors
    Russian Journal of Nonlinear Dynamics, 2016, vol. 12, no. 2, pp. 263-287
    Abstract          pdf  (3.54 Mb)
  • 36.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    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)

2015

  • 37.

    Bizyaev I. A., Kozlov V. V.

    Homogeneous systems with quadratic integrals, Lie–Poisson quasi-brackets, and the Kovalevskaya method
    Sbornik: Mathematics, 2015, vol. 206, no. 12, pp. 29–54
    Abstract          pdf  (481.65 Kb)
  • 38.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    Figures of equilibrium of an inhomogeneous self-gravitating fluid
    Celestial Mechanics and Dynamical Astronomy, 2015, vol. 122, no. 1, pp. 1-26
    Abstract          pdf  (651.34 Kb)
  • 39.

    Borisov A. V., Mamaev I. S., Kilin A. A., Bizyaev I. A.

    Qualitative Analysis of the Dynamics of a Wheeled Vehicle
    Regular and Chaotic Dynamics, 2015, vol. 20, no. 6, pp. 739-751
    Abstract          pdf  (445.93 Kb)
  • 40.

    Bizyaev I. A., Borisov A. V., Kazakov A. O.

    Dynamics of the Suslov Problem in a Gravitational Field: Reversal and Strange Attractors
    Regular and Chaotic Dynamics, 2015, vol. 20, no. 5, pp. 605-626
    Abstract          pdf  (640.12 Kb)
  • 41.

    Borisov A. V., Mamaev I. S., Bizyaev I. A.

    The Jacobi Integral in Nonholonomic Mechanics
    Regular and Chaotic Dynamics, 2015, vol. 20, no. 3, pp. 383-400
    Abstract          pdf  (990.04 Kb)
  • 42.

    Bizyaev I. A., Bolsinov A. V., Borisov A. V., Mamaev I. S.

    Topology and Bifurcations in Nonholonomic Mechanics
    Russian Journal of Nonlinear Dynamics, 2015, vol. 11, no. 4, pp. 735–762
    Abstract          pdf  (561.73 Kb)
  • 43.

    Borisov A. V., Mamaev I. S., Bizyaev I. A.

    The Jacobi Integral in NonholonomicMechanics
    Russian Journal of Nonlinear Dynamics, 2015, vol. 11, no. 2, pp. 377-396
    Abstract          pdf  (1.9 Mb)
  • 44.

    Bizyaev I. A., Bolsinov A. V., Borisov A. V., Mamaev I. S.

    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)
  • 45.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    Hamiltonization of Elementary Nonholonomic Systems
    Russian Journal of Mathematical Physics, 2015, vol. 22, no. 4, pp. 444-453
    Abstract          pdf  (115.49 Kb)

2014

  • 46.

    Bizyaev I. A.

    Nonintegrability and Obstructions to the Hamiltonianization of a Nonholonomic Chaplygin Top
    Doklady Mathematics, 2014, vol. 90, no. 2, pp. 631–634
    Abstract          pdf  (203.47 Kb)
  • 47.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    The Dynamics of Three Vortex Sources
    Regular and Chaotic Dynamics, 2014, vol. 19, no. 6, pp. 694-701
    Abstract          pdf  (244.27 Kb)
  • 48.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    Superintegrable Generalizations of the Kepler and Hook Problems
    Regular and Chaotic Dynamics, 2014, vol. 19, no. 3, pp. 415-434
    Abstract          pdf  (300.95 Kb)
  • 49.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    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. 198-213
    Abstract          pdf  (241.48 Kb)
  • 50.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    The dynamics of three vortex sources
    Russian Journal of Nonlinear Dynamics, 2014, vol. 10, no. 3, pp. 319-327
    Abstract          pdf  (413.32 Kb)
  • 51.

    Bizyaev I. A.

    On a generalization of systems of Calogero type
    Russian Journal of Nonlinear Dynamics, 2014, vol. 10, no. 2, pp. 209-212
    Abstract          pdf  (237.84 Kb)
  • 52.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    Figures of equilibrium of an inhomogeneous self-gravitating fluid
    Russian Journal of Nonlinear Dynamics, 2014, vol. 10, no. 1, pp. 73-100
    Abstract          pdf  (492.78 Kb)

2013

  • 53.

    Bizyaev I. A., Tsiganov A. V.

    On the Routh sphere problem
    Journal of Physics A: Mathematical and Theoretical, 2013, vol. 46, no. 8, 085202, 11 pp.
    Abstract          pdf  (169.11 Kb)
  • 54.

    Borisov A. V., Mamaev I. S., Bizyaev I. A.

    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. 277-328
    Abstract          pdf  (2.69 Mb)
  • 55.

    Bizyaev I. A., Borisov A. V., Mamaev I. S.

    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. 547-566
    Abstract          pdf  (441.83 Kb)
  • 56.

    Bizyaev I. A., Kazakov A. O.

    Integrability and stochastic behavior in some nonholonomic dynamics problems
    Russian Journal of Nonlinear Dynamics, 2013, vol. 9, no. 2, pp. 257-265
    Abstract          pdf  (2.27 Mb)
  • 57.

    Borisov A. V., Mamaev I. S., Bizyaev I. A.

    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. 141-202
    Abstract          pdf  (7.91 Mb)

2012

  • 58.

    Bizyaev I. A., Tsiganov A. V.

    On the Routh sphere
    Russian Journal of Nonlinear Dynamics, 2012, vol. 8, no. 3, pp. 569-583
    Abstract          pdf  (299.77 Kb)

2011

  • 59.

    Bizyaev I. A., Ivanova T. B.

    Figures of equilibrium of liquid self-gravitating inhomogeneous mass
    Bulletin of Udmurt University. Mathematics. Mechanics. Computer Science, 2011, no. 3, pp. 142-153
    Abstract          pdf  (215.68 Kb)
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