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Normal Terms of Hamiltonian Systems

100%
Wąż P.
Acta Physica Polonica A
|
1996
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vol. 89
|
issue 4
467-479
EN
All the transformation matrices for a Hamiltonian with two and three degrees of freedom are found. They are calculated using algorithms for the linear normalization of Hamiltonian systems near the equilibrium point.
2
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Asymmetry Coefficients as Indicators of Chaos: Hyperchaotic Qi System

63%
Wąż P., Bielińska-Wąż D.
Acta Physica Polonica A
|
2013
|
vol. 123
|
issue 4
647-650
EN
Statistical properties of the hyperchaotic Qi system are studied. The theory, recently formulated and applied for the damped driven pendulum, is used in this investigation. Asymmetry coefficients, related to the statistical moments of distributions composed from the time-series, are shown to behave in a different way for periodic, chaotic and hyperchaotic solutions and are proposed as indicators of chaos and hyperchaos.
3
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Asymmetry Coefficients as Indicators of Chaos

63%
Wąż P., Bielińska-Wąż D.
Acta Physica Polonica A
|
2009
|
vol. 116
|
issue 6
987-991
EN
The aim of this paper is to present a new simple indicator of chaos derived from the dynamics of the motion. For this purpose statistical methods are used. A function describing the motion of the analyzed system (in the example under consideration, the time dependence of the angle of a damped driven pendulum, ω(t)) is recorded in time intervals t∊〈 T_{s}, T_{f_{k}}〉, k = 1, 2,...K, with T_{f_{k}} > T_{f_{k-1}}. Each of the recorded functions is considered as a statistical distribution. The asymmetry coefficients of the set of distributions form a series and their behavior in periodic and chaotic regions is compared. It is shown that the behavior of this series in the chaotic and in the periodic regimes is entirely different. The changes of the asymmetry coefficients for the periodic cases are very regular and for the chaotic ones - random. In periodic cases, the coefficients converge to zero when the length of the distribution increases.
4
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Periodic Motion of Rigid Body in Circular Orbit

63%
Niedzielska Z., Wąż P.
Acta Physica Polonica A
|
1997
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vol. 92
|
issue 3
481-489
EN
The periodic rotations of a symmetric rigid body close to the flat motions are analytically determined. Their orbital stability is investigated. Calculations are done up to the second order terms of a small parameter.
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