MOSCOW, January 29Scientists at Samara University have proposed a mathematical method that will allow one to analyze and prevent the chaotic angular motion of space nanosatellites. The research results were published in the journal Communications in Nonlinear Science and Numerical Simulation.
According to scientists, nanosatellites are usually launched into orbit as a passing load and ejected from launch containers without controlling the initial orientation and other parameters of angular motion. If “chaos in dynamics” appears, the nanosatellite begins to tumble randomly without achieving a regular orientation, the researchers explained.
Moreover, even natural small satellites can be subject to random rotation. For example, in 2015, NASA scientists found that Pluto's natural satellites Nyx and Hydra move in their orbits, performing chaotic rotation, swaying and constantly turning over.
Scientists from Samara National Research University named after Academician S.P. Korolev (Samara University) proposed a method that would analytically detect and prevent this phenomenon in the dynamics of nanosatellites.
They modified Melnikov's mathematical method used to obtain the criterion for the emergence of chaos, and studied its new aspects.
“”Melnikov's original method works only in cases where the system formally contains an oscillatory disturbance acting with a steady amplitude. A modification of the method allows it to be used in cases of natural damping,” explained Anton Doroshin, head of the department of theoretical mechanics at Samara University.
As the main example of using a new modification of the method, the motion of a modular nanosatellite was studied. As the university reported, the results showed that the use of the modification in specific calculations made it possible to determine important parameters of dissipation – energy dissipation due to internal processes.
According to scientists, this ultimately makes it possible to find the dynamic parameters of a nanosatellite that ensure spontaneous suppression of chaotic motion, which is very important for the practice of space flight.
According to scientists, this ultimately makes it possible to find the dynamic parameters of a nanosatellite that ensure spontaneous suppression of chaotic motion movement, which is very important for the practice of space flight.
In addition, as the scientists added, as part of the study under conditions of zero dissipation (“idealized case”), an analysis was carried out of the dependence of the intensity of chaos development on the frequency of disturbing oscillations 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 value of this dangerous frequency depends not only on the properties of the structure, but also contains a whole complex of parameters, including inertial mass quantities nanosatellite and its initial kinetic energy,” Doroshin noted. At the same time, he emphasized that the obtained estimate for the value of this frequency will need to be taken into account when designing space missions with nanosatellites.
Samara University named after. Koroleva is a participant in the Russian state program for supporting universities “Priority 2030” of the national project “Science and Universities”.
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