Analytical solution of the problem on an axisymmetric spacecraft attitude maneuver optimal with respect to a combined functional

In the quaternionic setting, we consider the problem of optimal control of a spatial attitude maneuver of a spacecraft viewed as a rigid body with one symmetry axis without a constraint on the control function. For the optimality criterion we use a functional combining the time and energy spent on turning the spacecraft. Based on the Pontryagin maximum principle for this problem, new analytical solutions are obtained in the classes of conical and generalized conical motions. Numerical examples are given.