Publications

Online First Articles

• 1.

  Vetchanin E. V., Artemova E. M.

  Control of the motion of a circular foil using attached sources and internal mechanisms
  Izvestiya Vysshikh Uchebnykh Zavedeniy. Applied Nonlinear Dynamics, 2025

  Abstract          pdf  (5.02 Mb)

  Целью работы является исследование задачи управления плоскопараллельным движением кругового профиля в идеальной жидкости за счет изменения интенсивности присоеденных источников и вращения внутреннего ротора. Методы. Для построения математической модели используется описание движения жидкости на основе комплексного потенциала, который позволяет вычислить силовое воздействие жидкости на движущееся тело. Для решения задачи управления используется допущение о кусочно-постоянной форме управляющих воздействий, что позволяет выполнить явное интегрирование уравнений движения аналитическими методами. Результаты. Построены уравнения плоскопараллельного движения кругового профиля (в общем случае неуравновешенного) с произвольным количеством присоединенных источников. Движение источников относительно профиля и их интенсивности задаются явными функциями времени. Выполнено явное интегрирование уравнений движения в случае уравновешенного профиля с одним присоединенным источником для кусочно-постоянных управлений. Заключение. Явные решения уравнений движения были использованы для построения маневров поворота на месте и продвижения. Сформулирован алгоритм перемещения профиля в окрестности заданной траектории на основе попеременного использования элементарных маневров. Предложенный алгоритм траекторного управления является конструктивным доказательством управляемости рассмотренной системы. Построенное таким образом решение задачи управления может использоваться в качестве основы для решения этой же задачи в случае гладких управлений.

  
  

  Keywords	the motion control, ideal fluid, circular foil, attached source
  Citation	Vetchanin E. V., Artemova E. M., Control of the motion of a circular foil using attached sources and internal mechanisms, Izvestiya Vysshikh Uchebnykh Zavedeniy. Applied Nonlinear Dynamics, 2025, https://doi.org/10.18500/0869-6632-003205
  DOI:	10.18500/0869-6632-003205
  Full text:	pdf  (5.02 Mb)
• 2.

  Kilin A. A., Karavaev Y. L.

  Experimental observation of stabilization of tippe top spinning on a vibrating plane
  Theoretical and Applied Mechanics, 2025

  Abstract          pdf  (840.04 Kb)

  
  

  Citation	Kilin A. A., Karavaev Y. L., Experimental observation of stabilization of tippe top spinning on a vibrating plane, Theoretical and Applied Mechanics, 2025, https://doi.org/10.2298/TAM241204001K
  DOI:	10.2298/TAM241204001K
  Full text:	pdf  (840.04 Kb)
• 3.

  Bizyaev I. A., Berdnikova A. S.

  Chaotic Dynamics and Stability Analysis of a Roller Bicycle
  Regular and Chaotic Dynamics, 2025

  Abstract          pdf  (2.53 Mb)

  We analyze the stability of the straight-line motion of the bicycle depending on the mass-geometric parameters of the bicycle and its translational velocity. We construct a region in phase space which corresponds to initial conditions under which the bicycle tends asymptotically to straight-line motion. To investigate the bifurcations of the periodic solutions of the system, we construct a chart of dynamical regimes on the plane of two parameters and a three-dimensional Poincaré map. We analyze the possibility of acceleration or deceleration of the bicycle when the angular velocity of the rotor periodically changes in time.

  
  

  Keywords:	bicycle, nonholonomic system, stability, Poincaré map, strange attractor
  Citation:	Bizyaev I. A., Berdnikova A. S., Chaotic Dynamics and Stability Analysis of a Roller Bicycle, Regular and Chaotic Dynamics, 2025, https://doi.org/10.1134/S1560354725540032
  DOI:	10.1134/S1560354725540032
  Full text:	pdf  (2.53 Mb)
• 4.

  Kilin A. A., Ivanova T. B., Yefremov K. S.

  Controlled Motion of a Wheeled Three-Link Vehicle: Theory and Experiment
  Rus. J. Nonlin. Dyn., 2026

  Abstract          pdf  (1.38 Mb)

  In this paper we examine the controlled motion of a three-link wheeled mobile robot on a horizontal plane. The motion of the system is induced by periodic oscillations of the outermost links relative to the central link in the horizontal plane. The dynamics of the robot is analyzed using two theoretical models. The first is a model of nonholonomic rolling which assumes motion without slipping at the points of contact. The second is a hybrid dynamical model which takes into account the possibility of alternation between nonholonomic rolling and motion with slipping along the axis of a wheel pair. An experimental investigation of the dynamics of the developed prototype with different controls is carried out. A comparative analysis is made of the data obtained in the course of a full-scale experiment and the results of numerical simulation based on both models considered. This comparative analysis is used to identify the limits of applicability of the nonholonomic model. It is shown that within these limits the nonholonomic model describes the real motion with good accuracy.

  
  

  Keywords:	nonholonomic constraint, wheeled vehicle, periodic control, constraint reaction force
  Citation:	Kilin A. A., Ivanova T. B., Yefremov K. S., Controlled Motion of a Wheeled Three-Link Vehicle: Theory and Experiment, Rus. J. Nonlin. Dyn., 2026, https://doi.org/10.20537/nd260101
  DOI:	10.20537/nd260101
  Full text:	pdf  (1.38 Mb)
• 5.

  Vetchanin E. V., Mokrushina L. N.

  Cases of Explicit Integration in the $N$-Source Problem
  Rus. J. Nonlin. Dyn., 2026

  Abstract          pdf  (3.54 Mb)

  The motion of $N$ point sources on a plane is considered. Equations of motion of this system are represented in Hamiltonian form with a Hamiltonian that is a multivalued function of coordinates. A detailed analysis is presented for the case of sources with zero total strength, where a reduction by two degrees of freedom is possible. For three sources of which two have identical strengths, an explicit solution to the reduced system (with one degree of freedom) is constructed. The trajectories of the reduced system always remain on the same single-valued branch of the Hamiltonian and arrive in finite time at a branching point of the Hamiltonian. This point corresponds to collision of two sources with strengths of opposite signs. An exception is the trajectories lying on an invariant manifold which contains a fixed point of the reduced system. This fixed point corresponds to an equilateral triangular configuration. For four sources of which two have identical positive strengths and the other two have identical negative strengths, a reduced system with two degrees of freedom is presented. It is shown that the reduced system admits three invariant manifolds, on which the motion is integrable. On the two manifolds the sources form a collinear configuration, and on the third manifold the sources are located at the vertices of a (convex or concave) deltoid. For the reduced system restricted to the invariant manifold we have constructed first integrals, phase portraits, and have identified singularities and fixed points.

  
  

  Keywords:	point sources, ideal fluid, explicit integration, reduction
  Citation:	Vetchanin E. V., Mokrushina L. N., Cases of Explicit Integration in the $N$-Source Problem, Rus. J. Nonlin. Dyn., 2026, https://doi.org/10.20537/nd260102
  DOI:	10.20537/nd260102
  Full text:	pdf  (3.54 Mb)