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This article is cited in 2 scientific papers (total in 2 papers)
Period Doubling Bifurcation in Rigid Body Dynamics
A. V. Borisova, N. N. Simakovb a 119899, Russia, Moscow Vorobevy Gory, Moscow State University, Faculty of Mechanics and Mathematics, Department of Theoretical Mechanics
b Udmurt State University, Faculty of Physics, Izhevsk, Russia
Abstract:
Taking a classical problem of motion of a rigid body in a gravitational field as an example, we consider Feigenbaum's script for transition to stochasticity. Numerical results are obtained using Andoyer-Deprit's canonical variables. We calculate universal constants describing "doubling tree" self-duplication scaling. These constants are equal for all dynamical systems, which can be reduced to the study of area-preserving mappings of a plan onto itself. We show that stochasticity in Euler-Poisson equations can progress according to Feigenbaum's script under some restrictions on the parameters of our system.
Received: 10.12.1996
Citation:
A. V. Borisov, N. N. Simakov, “Period Doubling Bifurcation in Rigid Body Dynamics”, Regul. Chaotic Dyn., 2:1 (1997), 64–74
Linking options:
https://www.mathnet.ru/eng/rcd971 https://www.mathnet.ru/eng/rcd/v2/i1/p64
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