Dynamics of the Suslov problem in a gravitational field: reversal and strange attractors

The paper considers the generalized Suslov problem with variable parameters and the influence of random perturbations on the dynamics of the system under consideration. The physical meaning of the Suslov problem is Chaplygin's sleigh, which moves along the inner side of the circle. In the case of a deterministic system, a brief review of the previously obtained results is made, the presence of chaotic dynamics in the system and such effects as the appearance of a strange attractor and noncompact (escaping) trajectories is shown. Moreover, the latter may indicate a possible acceleration in the system. The appearance of chaotic strange attractors occurs due to a cascade of bifurcations of doubling the period. We also consider the dynamics of a perturbed system which arises due to the addition of «white noise» modeled by the Wiener process to one of the equations. Changes in the dynamics of a perturbed system compared to an unperturbed one are studied: chaotization of periodic regimes, the appearance of noncompact trajectories, and the premature destruction of strange attractors. In this paper, phase portraits, maps for the period, graphs of system solutions, and a chart of dynamical regimes are constructed using the Maple software package and the software package «Computer Dynamics: Chaos» (/http://site4.ics.org.ru//chaos_pack).

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Dynamics of the nonholonomic Suslov problem under periodic control: unbounded speedup and strange attractors

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8121/ab7e52 ◽

2020 ◽

Vol 53 (18) ◽

pp. 185701 ◽

Cited By ~ 1

Author(s):

Ivan A Bizyaev ◽

Ivan S Mamaev

Keyword(s):

Strange Attractors ◽

Periodic Control ◽

Suslov Problem

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A one-dimensional self-gravitating stellar gas

Symposium - International Astronomical Union ◽

10.1017/s0074180900105261 ◽

1966 ◽

Vol 25 ◽

pp. 46-48 ◽

Cited By ~ 2

Author(s):

M. Lecar

Keyword(s):

Gravitational Field ◽

Phase Space ◽

Motion Picture ◽

Space Distribution ◽

Two Dimensional ◽

One Dimensional ◽

Phase Space Distribution ◽

Dimensional Phase Space ◽

The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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Polar Magnetic Field Reversals of the Sun in Maunder Minimum

International Astronomical Union Colloquium ◽

10.1017/s0252921100064472 ◽

2000 ◽

Vol 179 ◽

pp. 193-196

Author(s):

V. I. Makarov ◽

A. G. Tlatov

Keyword(s):

Magnetic Field ◽

Maunder Minimum ◽

The Sun ◽

Annual Rings ◽

Field Reversal ◽

Polar Magnetic Field ◽

Pine Trees ◽

Using Data ◽

Magnetic Field Reversal

AbstractA possible scenario of polar magnetic field reversal of the Sun during the Maunder Minimum (1645–1715) is discussed using data of magnetic field reversals of the Sun for 1880–1991 and the14Ccontent variations in the bi-annual rings of the pine-trees in 1600–1730 yrs.

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