Prediction of motion about the center of mass as an element of motion control system software for advanced spacecraft

The paper presents results of development and verification of algorithms for integrating rigid-body spacecraft motion about its center of mass. The algorithms were developed in high-level language С++ as prototypes and elements of algorithms for flight software controlling motion and navigation of advanced spacecraft. Five algorithms were developed for integration with constant step based on a modified Discrete Mozer-Veselov (DMV) lagrangian method and second-order Stormer-Verlet symplectic scheme. These algorithms provide integration-step accuracies of the 2nd, 4th, 6th, 8th and 10th orders for problems in Free Rigid Body (FRB) angular motion and improve prediction accuracy for Torqued Rigid Body (TRB) rotational motion caused by potential and nonpotential generalized forces. Potential forces include gravitational and, partially, aerodynamic forces. Also developed were two variable time-step integration algorithms that provide relative precision above the 10th order for smooth problems. To verify the algorithms, a package of interfacing software programs was developed in the Visual C++ and MATLAB environments. Scaling of phase variables, motion integrals and time was used. The paper provides brief descriptions of the algorithms and methods for their testing, verification results and recommendations for selecting accuracies, integration interval and step. Used as input data were inertial and mass properties of various configurations for the Russian Orbital Station, which is currently under design.