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
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For a Chaplygin sleigh moving in the presence of weak friction, we present and investigate two mechanisms of arising acceleration due to oscillations of an internal mass. In certain parameter regions, the mechanism induced by small oscillations determines acceleration which is on average one-directional. The role of friction is that the velocity reached in the process of the acceleration is stabilized at a certain level. The second mechanism is due to the effect of the developing oscillatory parametric instability in the motion of the sleigh. It occurs when the internal oscillating particle is comparable in mass with the main platform and the oscillations are of a sufficiently large amplitude. In the nonholonomic model the magnitude of the parametric oscillations and the level of mean energy achieved by the system turn out to be bounded if the line of the oscillations of the moving particle is displaced from the center of mass; the observed sustained motion is in many cases associated with a chaotic attractor. Then, the motion of the sleigh appears to be similar to the process of two-dimensional random walk on the plane.

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

Chaplygin sleigh with periodically oscillating internal mass
EPL, 2017, vol. 119, no. 6, 60008, 7 pp.
Abstract
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We consider the movement of Chaplygin sleigh on a plane that is a solid body with
imposed nonholonomic constraint, which excludes the possibility of motions transversal to the constraint element (“knife-edge”), and complement the model with an attached mass, periodically oscillating relatively to the main platform of the sleigh. Numerical simulations indicate the occurrence of either unrestricted acceleration of the sleigh, or motions with bounded velocities and
momenta, depending on parameters. We note the presence of phenomena characteristic to nonholonomic systems with complex dynamics; in particular, attractors occur responsible for chaotic
motions. In addition, quasiperiodic regimes take place similar to those observed in conservative nonlinear dynamics.

Citation:

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.

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. 886-890
Abstract
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From analysis of time series obtained on the numerical solution of a plane problem on the motion
of a body with an elliptic cross section under the action of gravity force in an incompressible viscous fluid, a
system of ordinary differential equations approximately describing the dynamics of the body is reconstructed.
To this end, coefficients responsible for the added mass, the force caused by the circulation of the velocity
field, and the resisting force are found by the least square adjustment. The agreement between the finitedimensional
description and the simulation on the basis of the Navier–Stokes equations is illustrated by
images of attractors in regular and chaotic modes. The coefficients found make it possible to estimate the
actual contribution of different effects to the dynamics of the body.

Citation:

Borisov A. V., Kuznetsov S. P., Mamaev I. S., Tenenev V. A., 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. 886-890