Analysis of Perturbed Motion near the Stability Boundary of a Rotating Spacecraft of the INTERBALL Auroral Probe Type

The instability of the rotation of a spacecraft with flexible rod antennas is considered. A nonlinear mathematical model of a rigid solid body with attached one-dimensional flexible elements is used for dynamic analysis. The stability regions are constructed in the plane of the dimensionless parameters of the spacecraftʹs structure. The analytical solution obtained for the linearized model enables us to describe the qualitative picture of the unstable nutation motion of the object near the stability boundary. The dynamic analysis at a great distance from the stability boundary is carried out with the help of two methods: the root-locus method for linearized equations, numerically implemented by means of the QR-algorithm, and numerical integration of the nonlinear equations of perturbed motion using the Kutta-Merson method. The hodographs describing the nutation motion of a spacecraft and the shift of the flexible antenna is visualized on the basis of a nonlinear mathematical model of the spacecraft, which takes into account its main dynamical peculiarities. The values of the model parameters correspond to the INTERBALL Auroral Probe spacecraft.