Period Doubling Bifurcation in Rigid Body Dynamics
Regular and Chaotic Dynamics, 1997, vol. 2, no. 1, pp. 64-74
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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.
Borisov A. V., Simakov N. N., Period Doubling Bifurcation in Rigid Body Dynamics, Regular and Chaotic Dynamics, 1997, vol. 2, no. 1, pp. 64-74