Accurate predictions of chaotic motion of a free fall disk

It is important to know the accurate trajectory of a free fall object in fluid (such as a spacecraft), whose motion might be chaotic in many cases. However, it is impossible to accurately predict its chaotic trajectory in a long enough duration by traditional numerical algorithms in double precision. In this paper, we give the accurate predictions of the same problem by a new strategy, namely, the Clean Numerical Simulation (CNS). Without loss of generality, a free-fall disk in water is considered, whose motion is governed by the Andersen-Pesavento-Wang model. We illustrate that convergent and reliable trajectories of a chaotic free-fall disk in a long enough interval of time can be obtained by means of the CNS, but different traditional algorithms in double precision give disparate trajectories. Besides, unlike the traditional algorithms in double precision, the CNS can predict the accurate posture of the free-fall disk near the vicinity of the bifurcation point of some physical parameters in a long duration. Therefore, the CNS can provide reliable prediction of chaotic systems in a long enough interval of time.

Automated summary

Research shows that accurate predictions of chaotic trajectories of free-fall objects can be achieved using the Clean Numerical Simulation (CNS), while traditional algorithms in double precision provide relatively poor predictions. The CNS can reliably predict the posture of free-falling objects near bifurcation points of physical parameters over a long duration.