A possible new way for stabilizing by smooth feedback-a rigid body under only one control torque

The author deals with the motion of a rigid body under only one control torque. The method is based on the construction of the exact analytical solution of the closed loop system in terms of its nonlinear eigenvalues and eigenvectors. In other words, this solution may be the trajectory that the system has to track. The expression of the applied smooth feedback simply comes from the compatibility conditions of the whole differential equations. The stability algebraic conditions are therefore deduced in terms of these eigenvalues.<>