Aerospace Instrument-Making Annotation << Back USE OF THE PATH FUNCTIONAL FOR SYNTHESIS OF OPTIMAL CONTROL OF SPACECRAFT ATTITUDE M.V. Levskii The problem of optimal control of a spacecraft reorientation from an arbitrary initial position into a prescribed final angular position is studied. For optimization we use a generalized integral index characterizing the complexity of the rotation trajectory from the viewpoint of the "path covered," which takes into account the different «weight» of the spacecraft axes in the sense of expenditures (for example, of angular momentum) needed to rotate the spacecraft by the same angle. An analytical solution of this problem is obtained on base of Pontryagin’s maximum principle. The solving the optimal control problem is based on the quaternion equation connecting the angular momentum vector and the orientation quaternion of the body coordinate system. Formalized equations are derived and computational expressions for constructing the optimal control program are given. The optimal control is presented in synthesis form – the synthesizing function has been found, and the dependence of control variables from phase coordinates is determined. Key words: spacecraft, optimal control, optimality criterion, attitude, control function, the transversality conditions. Contacts: E-mail: dp940@mail.ru Pp. 03-11.