http://arxiv.org/abs/1704.02015
[abridged] A model of planar oscillations of an oblate satellite is investigated in terms of the dependence of its dynamics on the true anomaly $f$. The model is represented in a three-dimensional phase space. Maximal Lyapunov exponent (mLE) is computed in a two-dimensional space of the angular initial conditions for various initial conditions $f_0$. It is showed that the phase flow in the full three-dimensional space is twisted with a period of $2\pi$, i.e. one orbital period, but the distribution and strength of chaos is unchanged, meaning that the character of motion does not change, but simply migrates through the phase space. The twist is in good agreement with bifurcation diagrams constructed against $f_0$, which reveal a complicated mixture of chaotic and quasiperiodic trajectories. The onset of chaos, usually attributed to overlapping of the major spin-orbit resonances, for a sufficiently high value of the satellite’s oblateness, $\omega^2$, is easily visible with a so called generalized bifurcation diagram, i.e. an mLE map in a mixed space of $\omega^2$ and the initial condition.
The equation of motion is transformed to a two-dimensional model in which $f$ is the independent variable. This allows to utilize the Hamiltonian formalism to its extent, first to examine the diffusion of a dense set of initial conditions in the (now two-dimensional) phase space, and second, to employ a control method of suppressing chaos. The latter allows to construct a control term an order of magnitude smaller than the potential to which it is added. The diffusion of the trajectory in the phase space is not only diminished, but turns the motion into strictly periodic.
M. Tarnopolski
Mon, 10 Apr 17
15/36
Comments: 27 pages, 15 figures