The reversal and chaotic attractor in the nonholonomic model of Chaplygin’s top

Borisov, Alexey V.; Kazakov, Alexey O.; Сатаев, И. Р.

doi:10.1134/s1560354714060094

Cited by 59 publications

(34 citation statements)

References 25 publications

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“…Another direction is to apply a similar approach to problems in various fields, such as biophysics, laser physics [29,30], nonholonomic mechanics [31][32][33][34]. Besides there are interesting situations with more complex chaotic dynamics [28,35,36].…”

Section: Resultsmentioning

confidence: 99%

From chaos to quasi-periodicity

et al. 2015

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Ensembles of several Rössler chaotic oscillators are considered. It is shown that a typical phenomenon for such systems is the emergence of different and sufficiently high dimensional invariant tori. The possibility of a quasi-periodic Hopf bifurcation and a cascade of such bifurcations based on tori of increasing dimension is demonstrated. The domains of resonance tori are revealed. Boundaries of these domains correspond to the saddle-node bifurcations. Inside the domains of resonance modes, torus-doubling bifurcations and destruction of tori are observed.MSC2010 numbers: 70K43, 65P20, 65P30, 34D08

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Section: Resultsmentioning

confidence: 99%

From chaos to quasi-periodicity

et al. 2015

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“…The discussion of this set of issues and of the dynamics of systems with servoconstraints on Lie groups forms the content of this paper. For modern methods and problems of nonholonomic systems (analogs of some of them in the presence of servoconstraints are considered in this paper) see also the following series of works [4][5][6][7][8][9][10][11].…”

Section: Kozlovmentioning

confidence: 99%

The dynamics of systems with servoconstraints. I

Козлов

2015

Regul. Chaot. Dyn.

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The paper discusses the dynamics of systems with Béghin's servoconstraints where the constraints are realized by means of controlled forces. Classical nonholonomic systems are an important particular case. Special attention is given to the study of motion on Lie groups with left-invariant kinetic energy and left-invariant constraints. The presence of symmetries allows one to reduce the dynamic equations to a closed system of differential equations with quadratic right-hand sides on a Lie algebra. Examples are given which include the rotation of a rigid body with a left-invariant servoconstraint -the projection of the angular velocity onto some direction fixed in the body is equal to zero (a generalization of the nonholonomic Suslov problem) -and the motion of the Chaplygin sleigh with servoconstraints of a certain type. The dynamics of systems with Béghin's servoconstraints is richer and more varied than the more usual dynamics of nonholonomic systems.MSC2010 numbers: 34D20, 70F25, 70Q05

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“…Для исследования возможных режимов движения была построена карта динамических показателей Ляпунова [31,32] на плоскости параметров μ, Φ (см. рис.…”

Section: карта показателей ляпунова бифуркационные диаграммыunclassified