Period Doubling Bifurcation in Rigid Body Dynamics

    1997, Volume 2, Number 1, pp.  64-74

    Author(s): Borisov A. V., Simakov N. N.

    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.
    Citation: Borisov A. V., Simakov N. N., Period Doubling Bifurcation in Rigid Body Dynamics, Regular and Chaotic Dynamics, 1997, Volume 2, Number 1, pp. 64-74

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