Modeling of the perturbed motion of a rigid body in a resistive medium
DOI:
https://doi.org/10.37069/3154-8229-2026-40-3Keywords:
hodograph, information technology, the moment of momentum vector, modeling, numerical research, process visualizationAbstract
The modeling of a body’s motion under external perturbation requires precise computation of the influence of force factors. Information technologies provide effective methods for creating such models, visualizing results, and analyzing the behavior of objects in dynamic environments. These problems arise in the study of orientation and stabilization of spacecraft. This work models the rapid rotational motion of a dynamically asymmetric rigid body about its center of mass under the action of a resistance torque. The surrounding medium produces weak resistance. The paper proposes the use of an adaptive combined model of environmental resistance. Combined resistance models are widely studied in mechanics, physics, and engineering - particularly in the contexts of ballistics, hydrodynamics, aerodynamics, and biomechanics. The study is conducted in a dimensionless form for a multiparameter system of equations. A custom numerical computation package was developed for the constructed mathematical model of the rigid body. The numerical simulation makes it possible to obtain the function describing the variation of the kinetic moment vector in rotational motion. An analysis is carried out to study the influence of system parameters on the motion of the body relative to its center of mass. A qualitative picture is obtained showing how dimensionless parameters of the disturbance torque affect the shape of the kinetic moment vector hodograph. To analyze the motion, the hodograph of the kinetic moment vector will be simulated for the proposed model. The shape of the hodograph provides insight into the type of rotational motion occurring- whether it is stable, precessional, nutational, or unstable. Today, hodograph analysis is a standard step in modeling rotational motion for CubeSats, interplanetary probes (such as Voyager), and even space telescopes (such as Hubble).The hodograph of the kinetic moment vector is modeled in three-dimensional space for various parameter values. To construct 3D objects based on the numerical results, custom software was developed using DirectX technology in the C# programming language, simulating a virtual laboratory for numerical experiments. A criterion for the occurrence of different types of hodographs has been obtained.
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