Scientists from Samara University have proposed the mathematical method for analyzing and preventing chaotic angular motion of space nanosatellites. The research results are published in the journal “Communications in Nonlinear Science and Numerical Simulation”.

According to the scientists, nanosatellites are usually launched into orbit as way cargo and thrown out of launcher barrel without controlling their initial orientation and other angular motion parameters. The researchers explained that, in case of “chaos in dynamics”, the nanosatellite begins to tumble randomly, without achieving regular orientation.

Moreover, even natural small satellites can be subject to chaotic rotation. For example, in 2015, NASA scientists found that Pluto’s natural satellites Nix and Hydra move in their orbits, chaotically rotating, swaying and constantly turning over.

Scientists from Samara National Research University have proposed the method that will analytically detect and prevent this phenomenon in nanosatellite dynamics.

They modified the mathematical method of Melnikov, used to obtain a criterion for chaos occurrence, and studied its new aspects.

“The original method of Melnikov works only in cases when in the system, there is formally oscillatory disturbance with a steady-state amplitude. The modification makes it possible to apply the method in cases of natural attenuation”, explained Anton Doroshin, Head of the Department of Theoretical Mechanics at Samara University.

Motion of a modular nanosatellite was studied as the main example of applying this new modification of the method. According to our source within the University, the results showed that applying the modification in specific calculations made it possible to determine important parameters of dissipation – energy dissipation due to internal processes.

According to scientists, ultimately this allows finding the dynamic parameters for a nanosatellite, providing spontaneous suppression of chaotic motion, which is very important for the practice of space flight.

According to scientists, ultimately this allows finding the dynamic parameters for a nanosatellite, providing spontaneous suppression of chaotic motion, which is very important for the practice of space flight.

Besides, as part of the study under conditions of zero dissipation (“the idealized case”), the researchers analyzed the dependence of chaos-development intensity on disturbing-oscillation frequency in the mechanical system of the nanosatellite. The analysis showed that the system has the most dangerous frequency of disturbances, which can lead to maximum chaotic effects.

“The magnitude of this dangerous frequency not only depends on properties of the structure, but also contains a whole range of parameters, including mass-inertia values of the nanosatellite and its initial kinetic energy”, noted Doroshin. Herewith, he stressed that the obtained value for this frequency will need to be taken into account when space missions with nanosatellites are designed.
Samara University is a participant in the Russian State University-Support Program “Priority 2030” of the National Project “Science and Universities”.

Source: ria.ru