Optimal control of an angular motion of a rigid body during infinite and finite time intervals

摘要

This paper discusses the problem of optimal control of uniform angular motion of a rigid body containing an ideal fluid during both finite and infinite time intervals is studied by using Lyapunov–Bellman technique. Using Bellman equation the optimal control moments ensuring asymptotic stability of desired motion in both cases are obtained as non-linear functions of the phase coordinates and time. We are not concerned with the attitude of the body and consider only the evolution of the angular velocity as described by Euler’s equations. The square of the Euclidean norm of the perturbation of the angular velocity in both cases is estimated as a transcendental function of time.