Мodeling the deployment of rod structures as multilink pendulums under microgravity conditions

A new approach to modeling the transformation of rod structures in microgravity by investigating elements of their frameworks, represented as multi-link pendulums. A geometric model is presented for the deployment of such structures under the influence of pulsed thrusts from jet engines mounted at the endpoints of the links. The deployment mechanism is based on initiating inertial motion without continuous external control after a brief impulse application. The dynamics of the deployment process are described using Lagrange’s equations of the second kind, with particular emphasis on adapting the formulation to microgravity conditions, where potential energy can be considered negligible. This enables accurate modeling of structure deployment driven solely by kinetic energy, without further external control. As a result of the impulse action, the pendulum deploys by inertia, justifying the use of the term «inertial deployment method» for the frame. Mathematical models and a computer animation method are developed to predict the time evolution of link positions and to determine the fixation moment («stop code») for achieving the desired structure geometry. The influence of impulse magnitude errors on deployment accuracy is studied, and acceptable tolerance limits are established to maintain a satisfactory configuration. Test examples are provided for the deployment of double-link and four-link pendulums, as well as special configurations such as the Magdeburg pendulum and the Thomson-Tait pendulum. The obtained results are well-suited for animation to visualize the dynamics of rod structure formation—for example, illustrating the deployment of support frameworks for solar mirrors or space antennas. The proposed methods allow for the simplification of deployment technologies for large space objects, eliminating the need for complex electromechanical drives and thus reducing the mass and cost of space missions.