On the Differential Equation for the Square Modulus of the Extremal Angular Velocity Vector in the Least-Energy Reorientation Problem for a Circular Top

Abstract

We investigate the optimal control problem for the reorientation of a perfectly rigid circular top. For the criterion of the maneuver’s efficiency, we take the integral-square functional characterizing the total energy consumption. The control is the principal momentum of the applied external forces. In this problem, we obtain (for the first time) a scalar nonlinear differential equation such that its solution characterizes the second power of the absolute value of the extremal angular velocity vector. For polynomials depending on time, the family of solutions of the equation is considered. Numerical examples are provided.