Evgeniya Mikishanina
Publications:
Mikishanina E. A.
Dynamics of a Controlled Articulated $n$-trailer Wheeled Vehicle
2021, Vol. 17, no. 1, pp. 39-48
Abstract
This article is devoted to the study of the dynamics of movement of an articulated n-trailer
wheeled vehicle with a controlled leading car. Each link of the vehicle can rotate relative to its
point of fixation. It is shown that, in the case of a controlled leading car, only nonholonomic
constraint equations are sufficient to describe the dynamics of the system, which in turn form
a closed system of differential equations. For a detailed analysis of the dynamics of the system,
the cases of movement of a wheeled vehicle consisting of three symmetric links are considered,
and the leading link (leading car) moves both uniformly along a circle and with a modulo variable
velocity along a certain curved trajectory. The angular velocity remains constant in both cases.
In the first case, the system is integrable and analytical solutions are obtained. In the second
case, when the linear velocity is a periodic function, the solutions of the problem are also periodic.
In numerical experiments with a large number of trailers, similar dynamics are observed.
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Borisov A. V., Mikishanina E. A.
Dynamics of the Chaplygin Ball with Variable Parameters
2020, Vol. 16, no. 3, pp. 453-462
Abstract
This work is devoted to the study of the dynamics of the Chaplygin ball with variable
moments of inertia, which occur due to the motion of pairs of internal material points, and
internal rotors. The components of the inertia tensor and the gyrostatic momentum are periodic
functions. In general, the problem is nonintegrable. In a special case, the relationship of the
problem under consideration with the Liouville problem with changing parameters is shown.
The case of the Chaplygin ball moving from rest is considered separately. Poincaré maps are
constructed, strange attractors are found, and the stages of the origin of strange attractors are
shown. Also, the trajectories of contact points are constructed to confirm the chaotic dynamics
of the ball. A chart of dynamical regimes is constructed in a separate case for analyzing the
nature of strange attractors.
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Vetchanin E. V., Mikishanina E. A.
Vibrational Stability of Periodic Solutions of the Liouville Equations
2019, Vol. 15, no. 3, pp. 351-363
Abstract
The dynamics of a body with a fixed point, variable moments of inertia and internal rotors
are considered. A stability analysis of permanent rotations and periodic solutions of the system is
carried out. In some simplest cases the stability analysis is reduced to investigating the stability
of the zero solution of Hill’s equation. It is shown that by periodically changing the moments of
inertia it is possible to stabilize unstable permanent rotations of the system. In addition, stable
dynamical regimes can lose stability due to a parametric resonance. It is shown that, as the
oscillation frequency of the moments of inertia increases, the dynamics of the system becomes
close to an integrable one.
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