Analytical Quasi-Optimal Algorithm for Program Control of an Attitude of an Axisymmetric Spacecraft

The classical problem of optimal, in the sense of minimum of energy costs, program rotation of a spacecraft as a rigid body with one axis of symmetry under arbitrary boundary conditions is considered. With the help of variable substitutions, the original problem is simplified to the problem of optimal rotation of a rigid body with a spherical mass distribution containing one additional scalar differential equation. Within the bounds of the Poinsot concept of interpreting the angular motion of a rigid body around a fixed point, using the Pontryagin maximum principle, a quasi-optimal analytical solution of the problem is obtained. Numerical examples showing the proximity of the quasi-optimal solution to the optimal one are described.