Closed-Form Solutions for Single-Axis Slew Maneuvers Under a Fixed Final Time Constraint

This paper addresses a single-axis rotation problem in diverse space applications. In the problem, spin-to-spin boundary conditions, a finite jerk constraint, and a fixed final time constraint are considered. The objective is to find a path which maximizes the stabilization period under the given state boundary conditions and path inequality constraints. The optimal control problem is converted into a switching time design problem, and the unknown parameters are calculated analytically by solving the quartic, the cubic, or the quadratic equation. The proposed computational procedures are explained through numerical examples and the closed-form solutions are verified.