Mathematical Law for Mars Atmospheric Descent

A new mathematical law for controlling the rotation of spacecraft during descent into the Martian atmosphere has been derived by a scientist from Samara University. Its application will help safely deliver payloads—such as a small rover or scientific equipment—to the planet's surface. The findings are presented in the journal "Mechatronics, Automation, Control."

Stabilizing the rotational motion of a spacecraft before deploying braking parachutes requires controlling at least five parameters: three components of angular velocity and two orientation angles during descent in the planet's atmosphere, explained the study's author, Vladislav Lyubimov, head of the Department of Higher Mathematics at Samara University. The asymmetry of the vehicle can significantly influence the values of these parameters, he added.

"During the descent of a spacecraft in the Martian atmosphere, there is a flight segment with uncontrolled rotational motion. The presence of small force factors arising from slight vehicle asymmetry can lead to incorrect activation of the braking system," Lyubimov explained.

The scientist proposed a new mathematical law that will make descent in the Martian atmosphere more predictable. This new law for controlling the rotational motion of spacecraft with low asymmetry in the Martian atmosphere enables stabilization based on three components of angular velocity and two orientation angles of the vehicle, the study's author clarified.

"The distinctive feature of the new result is that it is more general than previously obtained analogues. At the same time, fewer approximate mathematical transformations were required for its synthesis, making the control law more precise," the researcher noted.

In the course of the work, well-known equations of spacecraft motion were applied, along with the method of linearizing nonlinear systems. The classical optimization method—dynamic programming—was also used, added Lyubimov.

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Source: ria.ru